Question

38. If a population is not normally distributed, the distribution of the sample means for a given sample size n will
A. take the same shape as the population                       
B. approach a normal distribution as n increases
C. be positively skewed
D. be negatively skewed
E. none of the above

39. A random sample of 66 observations was taken from a large population. The population proportion is 12%. The probability that the sample proportion will be more than 17% is

A. 0.0568
B. 0.8944
C. 0.1056       
D. 0.4222
E. None of the above

40. The scores on a certain test are normally distributed with mean 61 and standard deviation 3. What is the probability that a sample of 100 students will have a mean score more than 61.3?

A. 0.4602      
B. 0.3413
C. 0.8413
D. 0.1587      
E. none of the above.

Answer 1

(38)

Correct option:

B.   approach normal distribution as n increases

(39)

n = 66

P = 0.12

Q = 1- P= 0.88

SE =

To find P(p > 0.17):
Z= (0.17 -0.12)/0.04 = 1.25

Table of Area Under Standard Normal Curve gives area = 0.3944

So,

P(p > 0.17) = 0.5 - 0.3944 = 0.1056

So,

Correct option:

C.   0.1056

(40)

n = 100

= 61

= 3

SE = /

= 3/ = 0.3

To find P(>61.3)
Z= (61.3 - 61)/3 = 0.1

Table of Area Under Standard Normal Curve gives area = 0.0398

So,

P( > 61.3) = 0.5 - 0.0398 = 4602

So,

Correct option:

A.    0.4602