Question

A normal distribution has a mean of 15 and a standard deviation of 4. What percent of values are from 15 to 23

Answer 1

47.72%

Explanation:

Given

Mean (u) = 15

SD = 4

P(15<x<23) =
`P((x-u)/(\sigma)<z<(x-u)/(\sigma))`

=
`P((15-15)/(4)<z<(23-15)/(4))\\`

=P(0<z< 2)

=P(z<2) - P(z<0)

Use standard normal table to find probability of the z score

= 0.9772 - 0.5

= 0.4772
`\approx\\` 47.72%