Answer:0.0499
Step-by-step explanation:
Let x be a random variable that represents the salary for a data scientist.
Given: Average salary for a data scientist [tex]\mu=\$83105[/tex]
standard deviation [tex]\sigma=\$10503[/tex]
Sample size : n= 31
The probability that the mean salary of 31 randomly selected data scientists is less than $80,000.
[tex]P(\overline{X}<80000)=P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{80000-83105}{\dfrac{10503}{\sqrt{31}}})\\\\=P(z<-1.646)\ \ \ [z=(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(z<1.646)\ \ \ [P(Z<-z)=1-P(Z<z)]\\\\=1-0.9501= 0.0499[/tex]
Hence, the required probability = 0.0499.
What is the measure of an angle if the measures of its two adjacent supplementary angles add up to 100°?
The answer is not 80 btw
Explanation:
Let x be the unknown angle we want to find.
Let y be adjacent and supplementary to x. This means x+y = 180
Let z also be adjacent and supplementary to x. So x+z = 180 also
Subtracting the two equations leads to y-z = 0 and y = z. So effectively we've proven the vertical angle theorem.
Since the supplementary angles to x add to 100, we know that y+z = 100. Plug in y = z and solve for z
y+z = 100
z+z = 100
2z = 100
z = 100/2
z = 50
Therefore,
x+z = 180
x+50 = 180
x = 180-50
x = 130
Answer:
130°
Step-by-step explanation:
Let x be the unknown angle we want to find.
Let y be adjacent and supplementary to x. This means x+y = 180
Let z also be adjacent and supplementary to x. So x+z = 180 also
Subtracting the two equations leads to y-z = 0 and y = z. So effectively we've proven the vertical angle theorem.
Since the supplementary angles to x add to 100, we know that y+z = 100. Plug in y = z and solve for z
y+z = 100
z+z = 100
2z = 100
z = 100/2
z = 50
Therefore,
x+z = 180
x+50 = 180
x = 180-50
x = 130
Assume that SAT scores are normally distributed with mean 1518 and standard deviation 325. Round your answers to 4 decimal placesa. If 100 SAT scores are randomly selected, find the probability that they have a mean less than 1500.b. If 64 SAT scores are randomly selected, find the probability that they have a mean greater than 1600c. If 25 SAT scores are randomly selected, find the probability that they have a mean between 1550 and 1575d. If 16 SAT scores are randomly selected, find the probability that they have a mean between 1440 and 1480.e. In part c and part d, why can the central limit theorem be used even though the sample size does not exceed 30?
Answer:
a. 0.2898
b. 0.0218
c. 0.1210
d. 0.1515
e. This is because the population is normally distributed.
Step-by-step explanation:
Assume that SAT scores are normally distributed with mean 1518 and standard deviation 325. Round your answers to 4 decimal places
We are using the z score formula when random samples
This is given as:
z = (x-μ)/σ/√n
where x is the raw score
μ is the population mean
σ is the population standard deviation.
n is the random number of samples
a.If 100 SAT scores are randomly selected, find the probability that they have a mean less than 1500.
For x = 1500, n = 100
z = 1500 - 1518/325/√100
z = -18/325/10
z = -18/32.5
z = -0.55385
Probability value from Z-Table:
P(x<1500) = 0.28984
Approximately = 0.2898
b. If 64 SAT scores are randomly selected, find the probability that they have a mean greater than 1600
For x = 1600, n = 64
= z = 1600 - 1518/325/√64.
z= 1600 - 1518 /325/8
z = 2.01846
Probability value from Z-Table:
P(x<1600) = 0.97823
P(x>1600) = 1 - P(x<1600) = 0.021772
Approximately = 0.0218
c. If 25 SAT scores are randomly selected, find the probability that they have a mean between 1550 and 1575
For x = 1550, n = 25
z = 1550 - 1518/325/√25
z = 1550 - 1518/325/5
z = 1550 - 1518/65
= 0.49231
Probability value from Z-Table:
P(x = 1550) = 0.68875
For x = 1575 , n = 25
z = 1575 - 1518/325/√25
z = 1575 - 1518/325/5
z = 1575 - 1518/65
z = 0.87692
Probability value from Z-Table:
P(x=1575) = 0.80974
The probability that they have a mean between 1550 and 1575
P(x = 1575) - P(x = 1550)
= 0.80974 - 0.68875
= 0.12099
Approximately = 0.1210
d. If 16 SAT scores are randomly selected, find the probability that they have a mean between 1440 and 1480
For x = 1440, n = 16
z = 1440 - 1518/325/√16
= -0.96
Probability value from Z-Table:
P(x = 1440) = 0.16853
For x = 1480, n = 16
z = 1480 - 1518/325/√16
=-0.46769
Probability value from Z-Table:
P(x = 1480) = 0.32
The probability that they have a mean between 1440 and 1480
P(x = 1480) - P(x = 1440)
= 0.32 - 0.16853
= 0.15147
Approximately = 0.1515
e. In part c and part d, why can the central limit theorem be used even though the sample size does not exceed 30?
The central theorem can be used even though the sample size does not exceed 30 because the population is normally distributed.
Which graph shows a proportional relationship between the number of hours of renting a canoe and the total amount spent to rent the canoe?
Answer:
Uh pick a graph that is straight line and passes through 0
Step-by-step explanation:
You don't have screenshot
Answer:
This would be simaler to the answer
Step-by-step explanation:
A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, 10. The values on the y axis are 0, 18, 36, 54, 72, and 90. Points are shown on ordered pairs 0, 0 and 2, 18 and 4, 36 and 6, 54 and 8, 72. These points are connected by a line. The label on the x axis is Number of Hours. The title on the y axis is Total Amount in dollars.
Solve for x in the expression:
3 + 2x + 5 =0
Answer:
x= -4
Step-by-step explanation:
3 + 2x + 5 = 0
8 + 2x = 0
2x = -8
2x/2 = -8/2
x= -4
The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. Test H0 : p=0.28 vs Ha : p<0.28 when the sample has n=800, and p^=0.217 with SE=0.01.
Required:
Find the value of the standardized z-test statistic.
Answer:
Z = -6.3
Step-by-step explanation:
Given that:
[tex]\mathbf{H_o :p= 0.28}[/tex]
[tex]\mathbf{H_o :p < 0.28}[/tex]
Since the alternative hypothesis is less than 0.28, then this is a left-tailed hypothesis.
Sample sixe n = 800
[tex]\hat p[/tex] = 0.217
The standard error [tex]S.E(p) = \sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]S.E(p) = \sqrt{\dfrac{0.28(1-0.28)}{800}}[/tex]
[tex]S.E(p) \simeq0.015[/tex]
Since this is a single proportional test, the test statistics can be computed as:
[tex]Z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]Z = \dfrac{0.217- 0.28}{0.01}[/tex]
Z = -6.3
help please!!!!! (QUESTION #3)!!!!!!!
2. An inaccurate clock loses
3.
minutes every 8 hours. How much time will the clock lose in one
week?
How much does Jimmy earn each week, and
how much does he save by week 4?
A. Jimmy earns $3 each week, and he has $12 by
week 4.
B. Jimmy earns $3 each week, and he has $10 by
week 4.
C. Jimmy earns $6 each week, and he has $12 by
week 4.
D. Jimmy earns $6 each week, and he has $10 by
week 4.
Answer:
we need more info to answer this question
Answer:
A.
Step-by-step explanation:
12 divided by 4 equals 3. So if he gets 3 dollars a week by the fourth week he should have 12 dollars. It could also be 4 times 3 equals 12.
BLANK% of 50 shirts is 2 shirts.
Answer:
4%
Step-by-step explanation:
2/50 is 4....I believe.
Which of the following is the mean of the sampling distribution
Solve for g.
g + (-5) = 27
answer: g=32 u should simplify
b. Multiply (3 x - 1) by (x + 1)
Answer:
(3x - 1)(x + 1) = 3x² + 2x - 1
Step-by-step explanation:
[tex] \rm \longrightarrow (3x - 1)(x + 1) \\ \\ \rm \longrightarrow 3x(x + 1) - 1(x + 1) \\ \\ \rm \longrightarrow (3x)(x) + (3x)(1) + ( - 1)(x) + ( - 1)(1) \\ \\ \rm \longrightarrow 3 {x}^{2} + 3x + ( - x ) + ( - 1) \\ \\ \rm \longrightarrow 3 {x}^{2} + 3x - x - 1 \\ \\ \rm \longrightarrow 3 {x}^{2} + 2x - 1[/tex]
Answer:
(3x - 1)(x + 1) = 3x² + 2x - 1
Step-by-step explanation:
got it right on edge
Please help im stuck
Answer:
B
Step-by-step explanation:
substitution because
if m∠3=m∠7, and m∠7=m∠6 you can substitute
m∠7 to m∠3 and get m∠3=m∠6
Help Number three please!!!
Step-by-step explanation:
108-ambulance
100- police
1098-child laber
Marine biologists have been studying the effects of acidification of the oceans on weights of male baluga whales in the Arctic Ocean. One of the studies involves a random sample of 16 baluga whales. The researchers want to create a 95% confidence interval to estimate the true mean weight of male baluga whales. Their data follow a normal distribution. The population standard deviation of weights of male baluga whales is ????=125 kg, and the researchers feel comfortable using this standard deviation for their confidence interval.
Assuming the relevant requirements are met, calculate the margin of error in estimating the true mean weight of male baluga whales in the Artic Ocean.
a. 15.31 kg
b. 51.40 kg
c. 61.25 kg
d. 80.49 kg
Answer:
c. 61.25 kg
Step-by-step explanation:
The margin of error in estimating the true mean weight of male baluga whales in the Artic Ocean.
a. 15.31 kg
b. 51.40 kg
c. 61.25 kg
d. 80.49 kg
Margin of Error Formula= z × Standard deviation/√n
95% confidence interval = 1.96
Standard deviation = 125kg
n = 16 samples
Margin of error= 1.96 × 125/√16
= 1.96 × 125/4
= 245/4
= 61.25kg
The margin of error in estimating the true mean weight of male baluga whales in the Artic Ocean is 61.25kg
Write 0.45 as a fraction.
Answer:
9/20
Step-by-step explanation:
0.45 = 45/100
45/100=9/20 (divide numerator and denominator by 5)
89.36 in word form i have it in expanded form not word form though pls help ??????????????????????????????????????????????????????????????????????///
Answer:
eighty-nine and thirty-six hundredths
or, simpler:
eighty-nine point thirty-six
or, even simpler:
eighty-nine point three six
Answer:
eighty-nine and thirty-six hundredths
Step-by-step explanation:
i need to know the answer to this is radical form
2. An inaccurate clock loses
3 1/2
minutes every 8 hours. How much time will the clock lose in one
week?
Answer: 588 min
24x7 x3.5
A can of paint will cover 400 square feet. What is the length of the edge of the largest square that can be painted with this can of paint?
In order to become a member at a gym, there is a $75 startup fee. You then have to pay $15 per month. Write an equation in slope-intercept form modeling this situation where y represents the total cost and x represents the number of months spent at the gym
Answer:
y = 15x +75
Step-by-step explanation:
15 is the number of months and changes based on how many months
75 doesn't change, remains constant.
what is the value of 6797999012
Answer:
6797999012
Step-by-step explanation:
Which equation correctly shows the relationship between the numbers 6,560 and 656?
Answer:
656×1000
Step-by-step explanation:
Please help on this math question! I will love to help back on anything and give brainliest
Answer:
the perimeter is 25.
Step-by-step explanation:
have a nice day!
Daniel bought a package of 12 water bottles for $6. Write an equation that relates the cost, c, of a package of water bottles to the number of bottles, b, in the package?
Answer:
c = 2b
Step-by-step explanation:
First, find the cost of one water bottle by dividing the total cost by the number of water bottles:
12/6
= 2
Then, set up an equation.
2b, where b is the number of bottles, represents the cost of the package of water bottles.
Set this equal to c, the cost, to create the equation.
c = 2b is the equation relating the cost to the number of bottles
Answer This math question and ill give brainliest
Answer:
16 miles
Step-by-step explanation:
there are 8 units between the points each unit is 2 miles so 8*2= 16
what is the equation of a line perpendicular to line with equation 2x-5y=5
Answer:
its -5
Step-by-step explanation:
88) 4 times a number decreased by 8 equals 40
A) x=80 B) x = 40 C) x=8
D) x = 12
How much sparkling water would you need to make 100 quarts of sparkling grape juice? (Recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water and 3/4 quarts of grape juice)
Answer:
66.6666
Step-by-step explanation
This is the answer because I found it up here and I got the answer right.
Whoever answers correctly gets brainlist.
Answer:
1.- 4/5 + 5/12= 1 and 13/60
2.- 5/6 + 6/12= 1 and 1/3
3.- 1/3 + 2/6= 2/3
4.- 7/8 + 8/10= 1 and 27/40