Complete the following:
Q1. If an original set of measurements is made in inches and has a mean of 36 and a variance of 144, what will be the mean, variance, and standard deviation if:
a) the unit is changed to feet?
b) 6 inches must be added to each measurement to correct an error?
c) The measurements are converted to centimeters (2.5 cm = 1 inch) and then 15 cm is subtracted from each measurement to correct an error?
Q2. Calculate the standard scores for each of the members of the following distribution of shoe sizes:
a) 5, 7, 7, 8, 9, 12
Q3. Determine the proportion of scores falling under the normal curve:
a) between z = -1.5 and z = +1.5
b) between z = 1 and z = 2
c) to the right of z = -.75
d) to the left of z = -2.58 and to the right of z = +2.58
Q4. Between what two z-scores lie the central 50% of scores in the standard normal distribution?
Q5. What proportion of a normal distribution with mean 42 and standard deviation of 8 is:
A: between 26 and 58?
B: greater than 66?
C. less than 34?
D. between 10 and 42?
E. Less than 36 or greater than 48?
F. Between 44 and 58?
Q6. Suppose someone scored an 8 on a statistics homework. The mean for the class was 5.64 and the standard deviation for the class was 1.10. In coming up with final grades for the class, the instructor realized she needed to convert the homework scores so that the mean is 100 and the standard deviation is 10. Your job is to convert the 8 so that it is on this new scale. What is the new score for this student?