A chip used in the production of particleboard (Question 4) has a 15% chance of containing excessive bark. What is the probability of having more than 860 bark-free chips in a batch of 1,000

Answer:

0.2

Step-by-step explanation:

Given that:

P(particleboard with excessive bark) = 0.15

The P(that particleboard do not have excessive bark) = 1 - 0.15

i.e the population proportion number of success p = 0.85

The sample size (n) is given to be = 1000

To find the P(X ≥ 860)

Since the sample size is large, we will apply the normal approximation of binomial distribution to treat this question.

The population mean [tex]\mu = n \times p[/tex]

[tex]\mu = 1000 \times 0.85[/tex]

[tex]\mu =850[/tex]

The population standard deviation [tex]\sigma = \sqrt{n*p(1-p)[/tex]

[tex]\sigma = \sqrt{1000*0.85*(1-0.85)}[/tex]

[tex]\sigma = \sqrt{1000*0.85*(0.15)}[/tex]

[tex]\sigma = \sqrt{127.5}[/tex]

[tex]\sigma = 11.2916[/tex]

Let X be the random variable which obeys a normal distribution;

Then;

[tex]P(X \ge 860) = P(Z\ge \dfrac{x- \mu}{\sigma})[/tex]

[tex]P(X \ge 860) = P(Z\ge \dfrac{860- 850}{11.2916})[/tex]

[tex]P(X \ge 860) = P(Z\ge \dfrac{10}{11.2916})[/tex]

P(X ≥ 860) = P(Z ≥ 0.8856)

P(X ≥ 860) = 1 - P(Z ≤ 0.8856)

From  z table

P(X ≥ 860) = 1 - 0.8122

P(X ≥ 860) = 0.1878

P(X ≥ 860) [tex]\simeq[/tex] 0.2

Thus, the probability of having more than 860 bark-free chips in a batch of 1,000 = 0.2

A triangle has interior measures of 20° and 90°. What is the measure of the third angle?

he first five multiples for the numbers 4 and 6 are shown below.

Multiples of 4: 4, 8, 12, 16, 20, . . .
Multiples of 6: 6, 12, 18, 24, 30, . . .

What is the least common multiple of 4 and 6?
2
4
12
24

For question 15-16, find the value of x that would prove y || z. State the conserve used to support your answer.

Find the amount of interest to be paid.
Principal: $780
Annual Rate of Interest: 12 1/2%
Time: 6 months

Use the formula: i = prt (principal, rate, time)

What is the answer plz!!!! I Will mark brainliest!!!!!!

A researcher claims that the variation in the salaries of elementary school teachers is greater than the variation in the salaries of secondary school teachers (the claim). A random sample of 30 elementary school teachers has a variance of $ 8324, and a random sample of 30 secondary school teachers has a variance of $2862. At α= 0.05, can the researcher conclude that the variation in the elementary school teachers' Salaries is greater than the variation in the secondary teachers' salaries? Use the P-value method.
Assume that all variables are normally distributed.

a. State the hypotheses and identify the claim.
b. Find the critical value.
c. Compute the test value.
d. Make the decision.
e. Summarize the results.

WHAT IS THE ANSWER PLZ I WILL MARK BRAINLIEST!!!

What are multiplication facts that equal 9

Kendra is buying a Nintendo Switch with a price tag of $300. The sales tax rate where Kendra is purchasing the
Switch is 9.5%. How much will Kendra pay altogether for the Switch?

PLZ HELP ME I BEG YOU !!!!!!!!!!!!!!

answeerrrrrrrr pleaseeeee C:

can anyone answer number 2? Thank you

HELLLPPPP PLEASSSSEEE &&& THANK UUUU

I need help with this please

Please help!!!!! Can show work I’m stuck !!!!!!!!!

You are canning 40 cups of applesauce. You have 20 glass jars, each of which will hold 134 cups of applesauce. Choose the correct explanation(s) that explain why you do not have enough jars.


You do not have enough jars because 20 jars will only hold 35 cups of applesauce.

You do not have enough jars because you have enough applesauce left to completely fill 2 more jars, and almost fill a third jar.

You do not have enough jars because you need a total of 40×134=70 jars.

You do not have enough jars because the 20 jars would need to hold 2 cups each, but each holds 14-cup less than that.

PLEASE HELP!
Find x - y less than 0.
A. - y - x
B. x - y
C. - x + y

Parallel lines r and s are cut by two transversals, parallel lines t and u. Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of u and r, 13, 14, 15, 16. Which angles are alternate interior angles with angle 3? Angle5 and Angle13 Angle7 and Angle15 Angle6 and Angle16 Angle8 and Angle14 Mark this an

The problem is in the picture

5/8 ÷ 1/4 help I will give brainalest ​

pls answer my question​

11 ^ 2 power equals what

3600
in standard
form

a vase costs $2 bridget has some money if she gets $4.45 more she can buy 5 vases how much money does she have

Part A and Part B for Max's car together cost $1,693 dollars, Part A cost $58 dollars
more than twice what Part B cost. How much did each part cost?

An elevator started at the first floor and went up 18 floors. It then came down 11 floors and went back up 16. At what floor was it stopped?

I NEED HELP ,PLEASEEEE!!!!!

Shonda goes to a restaurant with no more than $15 to spend. She buys a burger that costs $10.50 and one other item. Write an equation to express how much money Shonda spent at the restaurant.

A store had 50 bottles of olive oil. Each week, 40% of the olive oil bottles were sold and 20 new bottles arrived in shipments. Which recursive function best represents the number of bottles in the store, given that f(0) = 50?

rate of change of 15

ABCDE is a
regular pentagon
find the angles of ADC?​