Question

Provide an appropriate response.

The amount of rainfall in January in a certain city is normally distributed with a mean of 4.2 inches and a standard deviation of 0.4 inches. Find the value of the 25th percentile, rounded to the nearest tenth.

A) 3.9

B) 1.1

C) 4.0

D) 4.5

2) In a sandwich shop, the following probability distribution was obtained. The random variable x represents the number of condiments used for a hamburger. Find the mean and standard deviation for the random variable x.

x | P(x)

0 0.30

1. 0.40

2 0.20

3 0.06

4 0.04

A)	mean: 1.30; standard deviation: 1.54

B)	mean: 1.30; standard deviation: 2.38

C)	mean: 1.14; standard deviation: 1.04

D)	mean: 1.54; standard deviation: 1.30

Answer 1

(1)

Given that,

P(Z < -0.674) = 0.25

z = -0.674

Using z-score formula,

x = z * +

x = -0.674 * 0.4 + 4.2 = 3.93

25th percentile = 3.9

(2)

x	P(x)	x * P(x)	x2 * P(x)
0	0.3	0	0
1	0.4	0.4	0.4
2	0.2	0.4	0.8
3	0.06	0.18	0.54
4	0.04	0.16	0.64
Sum	1	1.14	2.38

Mean = = X * P(X) = 1.14

Standard deviation =

=X ² * P(X) - ²

=  2.38 - 1.14²

= 1.04

Option C)