Question

Question 1 of 21

The weights of all babies born at a hospital have a mean of 7.4 pounds and a standard deviation of 0.66 pounds. Assuming (n/N less than 0.05), the standard deviation of the sampling distribution of the mean weight of a sample of 32 babies born at this hospital, rounded to three decimal places, is:

    A. 0.102

    B. 0.117

    C. 0.129

    D. 0.198

Question 2 of 21

A continuous random variable x has a left-skewed distribution with a mean of 155 and a standard deviation of 28. The sampling distribution of the sample mean for a sample of 75 elements taken from this population is:

    A. approximately normal

    B. skewed to the right

    C. not normal

    D. skewed to the left

Question 3 of 21

The time spent commuting from home to work for all employees of a very large company has a normal distribution with a mean of 43.4 minutes and a standard deviation of 12.1 minutes. The probability, rounded to four decimal places, that the mean time spent commuting from home to work by a sample of 21 employees will be between 43.26 and 49.35 minutes is:

    A. 0.2031

    B. 0.3156

    C. 0.4216

    D. 0.5090

Question 4 of 21

You ask 2,500 actors in the Screen Actors Guild (SAG) if they have ever appeared in a production of Shakespeare's King Lear. 1,225 of them say ?yes?, while the others say ?no?. The value p is the proportion of the actors who have appeared in King Lear. You next draw a random sample of 11 actors from the SAG. What are the mean and standard deviation of the sample proportion? Round the mean to two decimal places and the standard deviation to four decimal places.

    A. The mean is 0.49, The standard deviation is 0.1217

    B. The mean is 0.49, The standard deviation is 0.1507

    C. The mean is 0.1225, The standard deviation is 0.1217

    D. The mean is 0.1225, The standard deviation is 0.1507

Answer 1

1)

std.dev = s/sqrt(n))
= 0.66/sqrt(32)
= 0.117

2)

approx. normal

3)
P(43.26 <x< 49.35)
= P((43.26 - 43.4 )/(12.1/sqrt(21)) < z <(49.35- 43.4 )/(12.1/sqrt(21))
= P(-0.05 <z< 2.25)
= 0.5090

4)

p =1225/2500 = 0.49
Mean is 0.49

std.dev = sqrt(p*(1-p)/n)
= sqrt(0.49 *(1-0.49)/11)
= 0.1507

B. The mean is 0.49, The standard deviation is 0.1507