Question

The amount of 60 t-shirts has a normal distribution with a mean of $12 and standard deviation of $2. What percentage of the bills were between $10 and $14?

Answer 1

Explanation:

The formula for normal distribution is expressed as

z = (x - u)/s

Where

x = cost of T- shirts

u = mean cost

s = standard deviation

From the information given,

u = $12

s = $2

We would determine the probability of the bills that were between $10 and $14. It is expressed as

P(10 lesser than x lesser than or equal to 14)

For x = 10,

z = (10 - 12)/2 = -2/2 = -1

Looking at the normal distribution table, the corresponding z score is 0.15866

For x = 14,

z = (14 - 12)/2 = 2/2 = 1

Looking at the normal distribution table, the corresponding z score is 0.84134

P(10 lesser than x lesser than or equal to 14)= 0.84134 - 0.15866 = 0.68268

The percentage of the bills that were between $10 and $14 is

0.68268×100 = 68.3%