Question

(Sample distributions) Heights of males at WSU are normally distributed with a mean of 70 inches and a standard deviation of 3.5 inches. You will randomly select 16 males at WSU at record the mean height.

(a) Explain why the men of your sample will likely not be the population mean of 70 inches.

(b) What is the mean of your sampling distribution of means?

(c) What is the standard deviation of your sampling distribution of means?

(d) The Central Limit Theorem says that the sampling distribution of means is normally distributed. Using this fact, find the probability that the mean of your sample will be at least 69 inches. (The mean and standard deviations for your sampling distribution are those calculated in parts (b) and (c). With those, you can just use a normal distribution calculator.) (e) Find the probability that the mean of your sample will be between 68.4 inches and 70.1 inches

Answer 1

Answer:        

(Sample distributions) Heights of males at WSU are normally distributed with a mean of 70 inches and a standard deviation of 3.5 inches. You will randomly select 16 males at WSU at record the mean height.

(a) Explain why the men of your sample will likely not be the population mean of 70 inches.

We randomly selected males from WSU, so our population is all males from WSU. This is not representation of all students in WSU.

(b) What is the mean of your sampling distribution of means?

Mean = 70 inches

(c) What is the standard deviation of your sampling distribution of means?

Standard error = sd/sqrt(n) = 3.5/sqrt(16)

= 0.875

(d) The Central Limit Theorem says that the sampling distribution of means is normally distributed. Using this fact, find the probability that the mean of your sample will be at least 69 inches. (The mean and standard deviations for your sampling distribution are those calculated in parts (b) and (c). With those, you can just use a normal distribution calculator.)

Z value for 69, z =(69-70)/0.875 = -1.14

P(mean x >=69) = P( z > -1.14)

= 0.8729

(e) Find the probability that the mean of your sample will be between 68.4 inches and 70.1 inches

Z value for 68.4, z =(68.4-70)/0.875 = -1.83

Z value for 70.1, z =(70.1-70)/0.875 = 0.11

P( 68.4< mean x< 70.1) = P( -1.83<z<0.11)

=P( z< 0.11) – P( z < -1.83)

=0.5438 -0.0336

=0.5102