Mathematics, 12.02.2021 06:10 jake56555

he heights of adults in a certain town have a mean of 65.42 inches with a standard deviation of 2.32 inches. A random sample of 144 adults living in the center of the town was selected and their mean height was found to be 64.82 inches. Find the probability that a sample of this size would have a mean of 64.82 inches or less.

Answers: 1

Show answers

Answers

Answer from: superstarsara5ouh83x

0.001 = 0.1% probability that a sample of this size would have a mean of 64.82 inches or less.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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.

The heights of adults in a certain town have a mean of 65.42 inches with a standard deviation of 2.32 inches.

This means that $\mu = 65.42, \sigma = 2.32$

Sample of 144:

This means that $n = 144, s = \frac{2.32}{\sqrt{144}} = 0.1933$

Find the probability that a sample of this size would have a mean of 64.82 inches or less.

This is the pvalue of Z when X = 64.82. So

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

By the Central Limit Theorem

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

$Z = \frac{64.82 - 65.42}{0.1933}$

Z = -3.1

Z = -3.1 has a pvalue of 0.001

0.001 = 0.1% probability that a sample of this size would have a mean of 64.82 inches or less.

Answer from: Quest

yes because there is exactly one y value for every x value

for function there can't be more than one value for every x value

Answer from: Quest

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

\/ \/ \/ \/

48 + 24 - 408 + 24 - 3

\ / \ /

72 - 432 - 3 = -363

Another question on Mathematics

Mathematics, 21.06.2019 13:30

Phillip had some bricks. he stacked them in 6 equal piles. which expression shows the number of bricks phillip put in each pile? let the variable m stand for the unknown number of bricks. m + 6 m÷6 m−6 6m

Answers: 3

Answer

Mathematics, 21.06.2019 20:00

For problems 29 - 31 the graph of a quadratic function y=ax^2 + bx + c is shown. tell whether the discriminant of ax^2 + bx + c = 0 is positive, negative, or zero.

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Type the correct answer in each box. use numerals instead of words. the average number of subscribers to an online magazine each year from 2010 to 2015 is given in the table below. the average number of subscribers to the online magazine in 2010 was the percent increase in the average number of subscribers in 2011 to the average number of subscribers in 2012 was %. the maximum average number of subscribers to the online magazine in the years shown was

Answers: 2

Answer

Mathematics, 21.06.2019 23:20

Write the equations in logarithmic form 7^3=343

Answers: 1

Answer

You know the right answer?

he heights of adults in a certain town have a mean of 65.42 inches with a standard deviation of 2.32...

Questions