Question

The mean number of pairs of shoes sold daily by a shoe store is 36 with a standard deviation of 3. On what percent of days would you expect the store to sell from 33 to 42 pairs of shoes?

Answer 1

81.9%

Explanation:

z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean = 36

σ is the population standard deviation = 3

For x = 33

z = 33 - 36/3

= -1

Probability value from Z-Table:

P(x = 33) = 0.15866

For x = 42

z = 42 - 36/3

= 2

Probability value from Z-Table:

P(x = 42) = 0.97725

The probability of days would you expect the store to sell from 33 to 42 pairs of shoes is

P(x = 42) - P(x = 33)

= 0.97725 - 0.15866

= 0.81859

Therefore, the percent of days would you expect the store to sell from 33 to 42 pairs of shoes is calculated as

0.81859 × 100

= 81.859%

Approximately = 81.9%