Mathematics, 21.04.2020 20:15 juliannabartra

Suppose a batch of metal shafts produced in a manufacturing company have a population standard deviation of 1.3 and a mean diameter of 208 inches. If 60 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Answers: 1

Show answers

Answers

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central 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:

$\mu = 208, \sigma = 1.3, n = 60, s = \frac{1.3}{\sqrt{60}} = 0.1678$

What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Lesser than 207.9.

pvalue of Z when X = 207.9. So

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

By the Central Limit Theorem

$Z = \frac{207.9 - 208}{0.1678}$

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

2*0.2743 = 0.5486

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Answer from: Quest

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.

In the figure below abd measures 37 degrees what is the measure of abc?

Answer from: Quest

Idk idk idk idk idk idk idk idk

Another question on Mathematics

Mathematics, 21.06.2019 13:00

Write a division equation you could use to find a, the number of miles ava is in charge of. what is the value of a? write your answer is simplist form

Answers: 1

Answer

Mathematics, 21.06.2019 15:00

7(x - 2) = 3(x + 4) solve the following equation. then enter your answer in the space provided using mixed number format.

Answers: 2

Answer

Mathematics, 21.06.2019 15:30

You have 6 dollars +12 pennies +to quarters + 4 dimes=2 nickels how much do you have

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

Over the last 8 nights, elyse earned the following in tips: {105, 120, 84, 95, 100, 132, 140}. if she earns $140 a night for the next four nights, which measure of center would increase more, the mean or median?

Answers: 3

Answer

You know the right answer?

Suppose a batch of metal shafts produced in a manufacturing company have a population standard devia...

Questions