A reading specialist wanted to estimate the mean word length, in number of letters, for an elementary school history textbook. The specialist took repeated random samples of size 100 words and
estimated the mean and standard deviation of the sampling distribution to be 4.9 letters and 0.15 letter, respectively.
Based on the estimates for the sampling distribution, which of the following provides the best estimates of the population parameters?

Answer:

a) 0.1038 = 10.38% probability that maximum speed is at most 49 km/h

b) 0.2451 = 24.51% probability that maximum speed is at least 48 km/h

c) 0.9876 = 98.76% probability that maximum speed differs from the mean value by at most 2.5 standard deviations

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean value 46.8 km/h and standard deviation 1.75 km/h.

This means that [tex]\mu = 46.8, \sigma = 1.75[/tex]

a. What is the probability that maximum speed is at most 49 km/h?

This is the pvalue of Z when X = 49. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{49 - 46.8}{1.75}[/tex]

[tex]Z = 1.26[/tex]

[tex]Z = 1.26[/tex] has a pvalue of 0.8962

1 - 0.8962 = 0.1038

0.1038 = 10.38% probability that maximum speed is at most 49 km/h.

b. What is the probability that maximum speed is at least 48 km/h?

This is 1 subtracted by the pvalue of Z when X = 48. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{48 - 46.8}{1.75}[/tex]

[tex]Z = 0.69[/tex]

[tex]Z = 0.69[/tex] has a pvalue of 0.7549

1 - 0.7549 = 0.2451

0.2451 = 24.51% probability that maximum speed is at least 48 km/h.

c. What is the probability that maximum speed differs from the mean value by at most 2.5 standard deviations?

Zscores between Z = -2.5 and Z = 2.5, which is the pvalue of Z = 2.5 subtracted by the pvalue of Z = -2.5

Z = 2.5 has a pvalue of 0.9938

Z = -2.5 has a pvalue of 0.0062

0.9938 - 0.0062 = 0.9876

0.9876 = 98.76% probability that maximum speed differs from the mean value by at most 2.5 standard deviations

Answer:

7

Step-by-step explanation:

I did the math on a calculator

Answer:

2.18ft

Step-by-step explanation:

what is the arc length of s in the figure below​

Length of the arc = theta/360 * 2πr

r is the radius = 1ft

theta = 125 degrees

Substitute into the formula

Length of the arc = 125/360 * 2(3.14)* 1

Length of the arc = 785/360

Length of the arc  = 2.18ft

Hence the length of the arc is 2.18ft

Answer:

5x-6 = 2x+9

3x = 15

x = 5

Then

MP=38

Hope it helps you!

Answer:

f(-5) = 13

Step-by-step explanation:

Substitute x with -5

f(-5) = -3 (-5) - 2

=> 15 - 2

=> 13

hope this helps and is right. p.s. i really need brainliest :)

if this is wrong then I am incredibly sorry!

Answer:

Here

Step-by-step explanation:

Answer:

50  moons can fit inside Earth.

Step-by-step explanation:

The Volume of Earth is  

1.09 × 10 ^12

cubic kilometres

The Volume of The Moon is  

2.18 x 10^ 10

cubic kilometers

Hence the number of Moons that can fit in Earth is

Step-by-step explanation:

Answer:

2/33

Step-by-step explanation:

Chance of rolling a 1 is 1/33, chance of rolling a 2 is also 1/33. so add the probabilities 1/33 + 1/33 =2/33

Answer: 4. 432 cm^2/2 = 216 cm^2

6. 309.76 mm^2

8. pi * 22^2 = 484pi (or, approximately 1,519.76) in^2

484/2 = 242pi or 759.88 in^2.

10. 297.84 in^2/2 = 148.92 in^2

Step-by-step explanation:

To find the area of a triangle, you take the base and multiply by the height, and then divide by 2. Hence giving me the answers I obtained in #4 and #10.

A square is equal on all sides, so you would just square the measurement of the one side.

To find the area of a circle, you would do pi times the radius^2. Since this is a semicircle, you actually should divide the number you got by 2. (Which is why I did so up above).

Answer: There’s nothing

Step-by-step explanation:

Answer:

for 13 Surface are= 2*(9*7.2+9*9+7.2*9)= 421 m cube

Answer:

::::::::::::::::

B. 900 km/h

A quadratic equation is written in the form of ax²+bx+c. The roots of the given quadratic equation are shown in options B and F.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The roots of a quadratic equation can be found using the formula,

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Given the quadratic equation 3x²-x+5 = 0. Comparing it with the general quadratic equation the value of a, b, and c will be 3, -1, and 5.

Now, if we substitute the values in the formula of the roots of the quadratic equation,

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(5)}}{2(3)}\\\\[/tex]

x = (1±√-59)/6

x = (1+√-59)/6, (1-√-59)/6

Hence, the roots of the given quadratic equation are shown in options B and F.

Learn more about Quadratic Equations here:

https://brainly.com/question/2263981

#SPJ2

Answer: 7

Step-by-step explanation:

14*1=14

14/2=7

Answer:$3570

Step-by-step explanation:

42000x0.035=1470

2100+1470=3570

Answer:

B import food from other countries

Answer:

Step-by-step explanation:

60 and 64 :)

Answer:

18/81

Step-by-step explanation:

the current fraction adds up to 11 so to get 99 you would need to multiply both the numerator and the denominator by 9 to get a sum of 99

so 2 x 9 = 18 and 9 x 9 =81

so answer is 18/81

Answer:

we have

circumference of sphere=12.4π

2πr=12.4π

r=12.4/2=6.2

now

volume of sphere=4/3×πr³=4/3×π×(6.2)³=161 is your answer [approximately]

he always gI've correct answer

Answer:

46 ≤ n ≤ 60   ( C )

Step-by-step explanation:

using the given null hypothesis to check if the samples differ from originally values

given that:  frequency ( f ) ≥ 5

N = 600

hence : n * 0.11 ≥ 5

therefore : n ≥ 45.45

next : also  n / N ≤ 0. 10

therefore: n  ≤  0.1 * 600

therefore all possible sizes will lie between  

46≤n≤60

Answer:

Step-by-step explanation:

there are 52 cards in a deck, there are 4 aces. This would create a fraction of 4/52. (using the probaility set up of what I want over the total of everything). I hope this helps!

Answer:

75 DVDs

Step-by-step explanation:

Unit rate: 1/5

1 week

5 dvds

15*5= 75

he has 75 dvds after 15 weeks :)

Answer:

b = 33m is the answer

Step-by-step explanation:

a = 44m

b = ?

c = 55m

According to the Pythagoras theorem,

a² + b² = c²

44² + b² = 55²

1936 + b² = 3025

b² = 3025 - 1936

b² = 1089

b = 33m

∴ b = 33m is the length of the missing leg.

Answer:

Fraction:[tex]\frac{5}{9}[/tex]

Percent: to the nearest percent 56% or 55.5555555556%

Step-by-step explanation:

There are nine total parts and 5 of those parts are shaded

You would divide 5 by 9 to get the percent then multiply it by 100

Answer:

5/9

or

45%

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The researcher did no prediction or any (possible)

Hope this helps :)

Answer:

127

Step-by-step explanation: