Question

The height of women in the US is normally distributed with mean (mu) = 65 inches...

The height of women in the US is normally distributed with mean (mu) = 65 inches and standard deviation (sigma) = 2.5 inches. A random sample of 15 women is chosen from all women in the US. Is the sampling distribution of the sample ( x - bar) mean normally distributed? Why?

A.

No because the standard deviation is too small

B.

No because x < 30

C.

Yes. Because x < 30

D.

Yes, because the original x distribution was normally distributed

Homework Answers

Answer #1

According to central limit theorem,

i) If distribution of random variable x is normal then the sampling distribution of sample mean is also normally distributed.

ii) If sample size n is large (n > 30) then the sampling distribution of sample mean is approximately normally distributed irrespective of the distribution of random variable x.

Here random variable X is height of women in the US.

X is normally distributed.

So, the sampling distribution of the sample mean is normally distributed.

Option D is correct.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The distribution of young woman's height is normally distributed with a mean of 65 inches and...
The distribution of young woman's height is normally distributed with a mean of 65 inches and a standard deviation of 2.5 between what height do 95% of young women fall and what percentage of young women are shorter and 65 68-95-99.7 rule The IQ score of seven graders normally distributed with a mean of 111 standard deviation of 11 what percentage IQ score above 144 in a sample of 75 students in a rural school none had scored above 144...
The height of women ages​ 20-29 is normally​ distributed, with a mean of 65 inches. Assume...
The height of women ages​ 20-29 is normally​ distributed, with a mean of 65 inches. Assume sigmaσ=2.6 inches. Are you more likely to randomly select 1 woman with a height less than 67.1 inches or are you more likely to select a sample of 15 women with a mean height less than 67.1 ​inches? 1. What is the probability of randomly selecting 1 woman with a height less than 67.1 inches? ___ (Round to four decimal places as​ needed.) 2....
The height of women in the United States has a mean of 65 inches and a...
The height of women in the United States has a mean of 65 inches and a standard deviation of 3.5 inches. Find the probability that a woman chosen at random will be within 3 inches of the mean.
Assume that the heights of women are normally distributed with a mean of 63.6 inches and...
Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. a) Find the probability that if an individual woman is randomly selected, her height will be greater than 64 inches. b) Find the probability that 16 randomly selected women will have a mean height greater than 64 inches.
An adult height in North America is normally distributed with a mean of 65 inches and...
An adult height in North America is normally distributed with a mean of 65 inches and a standard deviation of 3.5 inches. 1. Find the probability that the height is between 64 and 66 inches P(64<X<66) 2. Find the probability that the height is greater than 70 inches. P(X>70). 3. The middle 40% of heights fall between what two values? P(x1 < X < x2) so beyond lost on this one
If the heights of women are normally distributed with a mean of 65.0 inches and a...
If the heights of women are normally distributed with a mean of 65.0 inches and a standard deviation of 2.5 inches and the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. A male patient's height in this experiment is 71 inches. Answer the series questions below. (Formulas and explanations needed) (a) Determine the probability of finding a person of same gender as the patient to be exactly at patient's...
Assume that women's heights are normally distributed with a mean given by mu = 64.2in and...
Assume that women's heights are normally distributed with a mean given by mu = 64.2in and a standard deviation given by sigma = 2.4 in (a) 1 woman is randomly selected, find the probability that her is less than 65 in. (b) 33 women are randomly selectedfind the probability that they have a mean height less than 65 in.
The height of women ages? 20-29 is normally? distributed, with a mean of 63.9 inches. Assume...
The height of women ages? 20-29 is normally? distributed, with a mean of 63.9 inches. Assume sigmaequals2.4 inches. Are you more likely to randomly select 1 woman with a height less than 66.2 inches or are you more likely to select a sample of 10 women with a mean height less than 66.2 ?inches? Explain. LOADING... Click the icon to view page 1 of the standard normal table. LOADING... Click the icon to view page 2 of the standard normal...
The height of women ages​ 20-29 is normally​ distributed, with a mean of 64.5 inches. Assume...
The height of women ages​ 20-29 is normally​ distributed, with a mean of 64.5 inches. Assume σ=2.4 inches. Are you more likely to randomly select 1 woman with a height less than 66.2 inches or are you more likely to select a sample of 21 women with a mean height less than 66.2 ​inches? Explain. What is the probability of randomly selecting 1 woman with a height less than 66.2 ​inches ​(Round to four decimal places as​ needed.) What is...
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 65 inches and standard...
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 65 inches and standard deviation 5 inches. (a) What is the probability that an 18-year-old man selected at random is between 64 and 66 inches tall? (Round your answer to four decimal places.) (b) If a random sample of nineteen 18-year-old men is selected, what is the probability that the mean height x is between 64 and 66 inches? (Round your answer to four decimal places.) (c) Compare...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT