Question

In a recent survey of 655 working Americans ages 25–34, the average weekly amount spent on lunch was $44.60 with standard deviation $2.81. The weekly amounts are approximately bell-shaped.

18. Estimate the percentage of amounts that are between $36.17 and $53.03. and Estimate the percentage of amounts that are between $41.79 and $47.41.

Answer 1

a)

P(36.17 <X < 53.03) = ?

z = ( X - Mean ) / SD

For X = 36.17

z = ( 36.17 - 44.60) / 2.81

= -3

36.17 is 3 standard deviation below the mean.

For X = 53.03

z = ( 53.03 - 44.60) / 2.81

= 3

53.03 is 3 standard deviation above the mean.

According to empirical rule,

Approximately, 99.7% of the data falls in 3 standard deviation of the mean.

So,

P(36.17 < X < 53.03) = 99.7 %

b)

P(41.79 <X < 47.41) = ?

z = ( X - Mean ) / SD

For X = 41.79

z = ( 41.79 - 44.60) / 2.81

= -1

41.79 is 1 standard deviation below the mean.

For X = 47.41

z = ( 47.41 - 44.60) / 2.81

= 1

47.41 is 1 standard deviation above the mean.

According to empirical rule,

Approximately, 68% of the data falls in 1 standard deviation of the mean.

So,

P(41.79 < X < 47.41) = 68%