Mathematics, 24.03.2020 03:22 rainyshea72

The inside diameter of a randomly selected piston ring is a random variable with mean value 13 cm and standard deviation 0.08 cm. Suppose the distribution of the diameter is normal. (Round your answers to four decimal places.)(a) Calculate P(12.99 ≤ X ≤ 13.01) when n = 16.P(12.99 ≤ X ≤ 13.01) =(b) How likely is it that the sample mean diameter exceeds 13.01 when n = 25?P(X ≥ 13.01) =

Answers: 2

Show answers

Answers

Answer from: khalidalrasheedi2025

a) P(12.99 ≤ X ≤ 13.01) = 0.3840

b) P(X ≥ 13.01) = 0.3075

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the cental limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 13, \sigma = 0.08$

(a) Calculate P(12.99 ≤ X ≤ 13.01) when n = 16.

Here we have $n = 16, s = \frac{0.08}{\sqrt{16}} = 0.02$

This probability is the pvalue of Z when X = 13.01 subtracted by the pvalue of Z when X = 12.99.

X = 13.01

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{13.01 - 13}{0.02}$

Z = 0.5

Z = 0.5 has a pvalue of 0.6915

X = 12.99

$Z = \frac{X - \mu}{s}$

$Z = \frac{12.99 - 13}{0.02}$

Z = -0.5

Z = -0.5 has a pvalue of 0.3075

0.6915 - 0.3075 = 0.3840

P(12.99 ≤ X ≤ 13.01) = 0.3840

(b) How likely is it that the sample mean diameter exceeds 13.01 when n = 25?

P(X ≥ 13.01) =

This is 1 subtracted by the pvalue of Z when X = 13.01. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{13.01 - 13}{0.02}$

Z = 0.5

Z = 0.5 has a pvalue of 0.6915

1 - 0.6915 = 0.3075

P(X ≥ 13.01) = 0.3075

Answer from: Quest

the answer is "add 2y and y"

step-by-step explanation:

you need to collect the like terms first.

Answer from: Quest

In order to find the price per bar, we divide the price by the amount of bars. for the first one: 15.37/10 = $1.54 per barthe second package: 15.35/12 = $1.28 per bar.the 10-pack costs $1.54 per bar and the 12-pack costs $1.28 per bar. the 12-pack has the better price per bar.now, let's look at the price per ounce. we do this in a similar way. we find the total amount of ounces in the package, and divide the price by the number of ounces.in the first package, we multiply 10*2.1=21. we have 21 ounces in the first package. now we divide 15.37/21. in the first package, we have 0.73 dollars per ounce.now, let's look at the second package. we start by multiplying 1.4*12=16.8. there are 16.8 ounces in the package. now, we divide 15.35/16.8=0.91. so, in the second package, we have 0.91 dollars per ounce.the cost per ounce of the 10-pack is $0.73 and the cost per ounce of the 12-pack is $0.91. the first package has the better price per ounce.the better explanation is the second one, because i prefer the lower price per ounce, i think that the 1st pack is the better buy.

Another question on Mathematics

Mathematics, 21.06.2019 17:30

James adds two numbers a + b. sally adds the same two numbers but reverse the order b + a what property of addition assures us that james and sally will get the same sum

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

What is the effect on the graph of the function f(x) = x2 when f(x) is changed to f(x) − 4?

Answers: 1

Answer

Mathematics, 22.06.2019 00:30

Suppose that the function f is defined. , for all real numbers, as follows. _ \ 1/4x² -4 if x≠ -2 f(x)=< /_-1 if x=-2 find f(-5), f(-2), and f(4)

Answers: 3

Answer

Mathematics, 22.06.2019 04:30

Agroup of five people go out to eat and buy appetizers and main dishes they decide to split the bill so each person pays 20% of the total cost appetizers are $5 and main dishes are $10 write an expression to show how much each person pays explain it with how to solve the problem

Answers: 1

Answer

You know the right answer?

The inside diameter of a randomly selected piston ring is a random variable with mean value 13 cm an...

Questions

Mathematics, 25.07.2019 21:30

Which is the sum of the interior angles of an octagon?...