<img src="//img.wizedu.com/questions/e138b710-cddd-11ec-b542-9b7bb9a66004.jpg" title="1626232088410838.jpg" alt="7CB069AE-E873-4DD7-B52B-F0BF616C37C6.jpeg"/>A survey found that women's heights are normally distributed with mean \(63.6\) in. and standard deviation \(3.4\) in. The survey also found that men's heights are normally distributed with mean \(69.7\) in. and standard deviation \(3.1\) in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 64 in. Complete parts (a) and (b) below.a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park?The percentage of men who meet the height requirement is \(\square \%\). (Round to two decimal places as needed.)

Given:For women :Mean = <img src="//img.wizedu.com/questions/e1c26680-cddd-11ec-8b2f-63c2c6e8c61d.png"/> = 62.4Standard deviation = <img src="//img.wizedu.com/questions/e2434910-cddd-11ec-b987-c5a27fe7ee25.png"/> = 3.7Let X be the women's heights are normally distributed.For women :Mean = <img src="//img.wizedu.com/questions/e1c26680-cddd-11ec-8b2f-63c2c6e8c61d.png"/> = 69.1Standard deviation = <img src="//img.wizedu.com/questions/e2434910-cddd-11ec-b987-c5a27fe7ee25.png"/> = 3.6Let X be the men's heights are normally distributed<img src="//img.wizedu.com/questions/e2fdc060-cddd-11ec-972e-1530ef8ae3e7.png" title="1626338962126618.png" />Thereforea) The percentage of men who meet the height requirement is 7.70 %

Question

In: Other

Find the percentage of men meeting the height requirement

A survey found that women's heights are normally distributed with mean \(63.6\) in. and standard deviation \(3.4\) in. The survey also found that men's heights are normally distributed with mean \(69.7\) in. and standard deviation \(3.1\) in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 64 in. Complete parts (a) and (b) below.

a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park?

The percentage of men who meet the height requirement is \(\square \%\). (Round to two decimal places as needed.)

Expert Solution

Given:

For women :

Mean = = 62.4

Standard deviation = = 3.7

Let X be the women's heights are normally distributed.

For women :

Mean = = 69.1

Standard deviation = = 3.6

Let X be the men's heights are normally distributed

Therefore

a) The percentage of men who meet the height requirement is 7.70 %

Amanda K answered 2 years ago

5) The average height of women is ̄y = 64.5 inches, the average height of men...

5) The average height of women is ̄y = 64.5 inches, the average height of men is ̄y = 67.5 inches. For both the standard deviation is about s = 3 inches. (a) Suppose you take a sample of 4 women and 4 men. Construct a 95% CI for both. Do the confidence intervals overlap? (b) Now repeat using a sample of 225 men and 225 women. Do the confidence intervals overlap? (c) Can you explain what happened? Why is...

Women today are paid, on average, a percentage of every dollar paid to men. This percentage...

Women today are paid, on average, a percentage of every dollar paid to men. This percentage has risen over the years, but pay between genders is still not equal. To help address this unfair and unacceptable wage gap, the Lilly Ledbetter Fair Pay Act was signed on January 29, 2009, restoring the protection against pay discrimination that was stripped away by the Supreme Court’s decision in Ledbetter v. Goodyear Tire & Rubber Co. Read about the Lilly Ledbetter Fair Pay...

Are older men shorter than younger men? According to a national report, the mean height for...

Are older men shorter than younger men? According to a national report, the mean height for U.S. men is 69.4 inches. In a sample of 119 men between the ages between of 60 and 69 and, the mean height was 69.3 inches. Public health officials want to determine whether the mean height for older men is less than the mean height of all adult men. Assume the population standard deviation to be 2.58. Use the a=0.05 level of significance and...

T-Test A research team measured 70 American men’s height. The average height of these men is...

T-Test A research team measured 70 American men’s height. The average height of these men is 176cm and the sample variance is 16. Is the average height of American males different from 174cm? a) State the null and alternative hypotheses b) Compute the t-statistics c) Draw the statistical conclusion (at 95% confidence level)

A menswear manufacturer knows that the height of all men is normal with a mean of...

A menswear manufacturer knows that the height of all men is normal with a mean of 69 inches and a standard deviation of 3 inches. a) What proportion of all men have a height between 69 and 74 inches? b) What proportion of all men have a height between 67 and 74 inches? c) What is the 95th (and 99th) percentile of all men’s heights?

Suppose that the height of Australian men is normally distributed with a mean of 175cm and...

Suppose that the height of Australian men is normally distributed with a mean of 175cm and standard deviation of 5cm. i. What is the probability that a Australian man's height will be between 180cm and 190cm? ii. What is the probability that a Australian man's height will be less than 190cm? iii. Ten percent (10%) of Australian men were taller than what height?

You are curious if there is a difference between men and woman for the approval percentage...

You are curious if there is a difference between men and woman for the approval percentage of a politician. Out of 400 men 307 approve and out of 500 women 340 approve. (A) Find a 95% confidence interval for diffrence in proportion of men and women of the political candidate (B) Does Your interval overlap 0? What does this signify? (C) At the 5% significance level, test the claim that the proportion of men vs woman who approve of the...

. A bank has recently begun a new credit program. Customers meeting a certain credit requirement...

. A bank has recently begun a new credit program. Customers meeting a certain credit requirement can obtain a credit card accepted by participating area merchants that carries a discount. Past data show that about 35% of all applicants for this card are rejected. If we let X represent the number of applicants who are approved for this credit card, the probabilities for the values of X can be calculated using the binomial probability distribution. Please answer the following questions...

A large study of the heights of 880 adult men found that the mean height was...

A large study of the heights of 880 adult men found that the mean height was 70 inches tall. The standard deviation was 4 inches. If the distribution of data was normal, what is the probability that a randomly selected male from the study was between 66 and 78 inches tall? Use the 68-95-99.7 rule (sometimes called the Empirical rule or the Standard Deviation rule). For example, enter 0.68, NOT 68 or 68%..

Suppose the height of adult men in the US is roughly normally distributed with a mean...

Suppose the height of adult men in the US is roughly normally distributed with a mean of 80 inches and a standard deviation of 6 inches. (a) What is the probability of an adult male being taller than 70 inches? (b) Approximately 15% of adult men are shorter than how many inches?