Reference no: EM131720141

1) Find the following z values for the standard normal variable Z. Use Table 1. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

a. P(Z ≤ z) = 0.8605    

b. P(Z > z) = 0.8018   

c. P(-z ≤ Z ≤ z) = 0.86  

d. P(0 ≤ Z ≤ z) = 0.2235  

2) Let X be normally distributed with mean μ = 20 and standard deviation σ = 12. Use Table 1.

a. Find P(X ≤ 2). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

P(X ≤ 2)

b. Find P(X > 5). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

P(X > 5)

c.Find P(5 ≤ X ≤ 20). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

P(5 ≤ X ≤ 20)  

d. Find P(8 ≤ X ≤ 20). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

P(8 ≤ X ≤ 20)  

3) Let X be normally distributed with mean μ = 125 and standard deviation σ = 29. Use Table 1. 

a. Find P(X ≤ 100). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

P(X ≤ 100)   

b. Find P(95 ≤ X ≤ 110). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

P(95 ≤ X ≤ 110)   

c. Find x such that P(X ≤ x) = 0.440. (Round "z" value and final answer to 2 decimal places.)

x   =

d. Find x such that P(X > x) = 0.900. (Round "z" value and final answer to 2 decimal places.)

x   =

4) The average high school teacher annual salary is $43,000 (Payscale.com, August 20, 2010). Let teacher salary be normally distributed with a standard deviation of $18,000. Use Table 1.

a. What percentage of high school teachers make between $40,000 and $50,000? (Round "z" value and final answer to 2 decimal places.)

Percentage of high school teachers %  =

b. What percentage of high school teachers make more than $80,000? (Round "z" value and final answer to 2 decimal places.)

Percentage of high school teachers % =n: 03_22_2016_QC_CS-46434

5) The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 29 minutes and 11 minutes, respectively. Use Table 1.

a. Find the probability that a randomly picked assembly takes between 18 and 30 minutes. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Probability   =

b. It is unusual for the assembly time to be above 44 minutes or below 16 minutes. What proportion of assembly times fall in these unusual categories? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Proportion of assembly times   =