Question

A particular population, for which the frequency curve is bell-shaped (normal), has a mean of μ=100 and a standard deviation of σ=18. For samples of size n=36 consider the sampling distribution of the sample mean ("xbar").

Note that 18 36=3 and that

• 100±(1)(3)⟹97 to 103
• 100±(2)(3)⟹94 to 106
• 100±(3)(3)⟹91 to 109

According to the empirical rule, approximately _____ percent of samples of size 36 will produce a sample mean between 97 and 103.

Group of answer choices

90

95

99.7

None of the other choices represent a suitable response.

68

Answer 1

Answer = 68  

= 100, = 18, n= 36

for sampling distribution standard deviation is

100 ± ( 1 * 3 )⟹ 100 ± 3

100 ± 3 ⟹ 97 to 103

97 to 103 are the cutoff for 1 standard deviation bellow and 1 standard deviation above the mean.

according to empirical rule,

68 % of samples lie between 1 standard deviation ( 97 to 103 )

95 % of samples lie between 2 standard deviation ( 94 to 106 )

99.7% of samples lie between 2 standard deviation ( 91 to 109 )

normal curve for empirical rule is as follows