# Normal Distribution & Critical Z-Value

1.The net profit of an investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000. The probability that the investor's net profit will be between $12,000 and $15,000 is _____________.

a) 0.8413

b) 0.1859

c) 0.4967

d) 0.3413

2. When the rod shearing process at Stockton Steel is "in control" it produces rods with a mean length of 120 inches. Periodically, quality control inspectors select a random sample of 36 rods. If the mean length of sampled rods is too long or too short, the shearing process is shut down. Sarah Shum, Director of Quality Programs, chose a 0.05 level of significance for this test. The critical z values are _________.

a) -1.75 and 1.75

b) -1.96 and 1.96

c) -1.645 and 1.645

d) -2.33 and 2.33

https://brainmass.com/statistics/probability/normal-distribution-critical-z-value-101448

#### Solution Preview

1.The net profit of an investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000. The probability that the investor's net profit will be between $12,000 and $15,000 is _____________.

a) 0.8413

b) 0.1859

c) 0.4967

d) 0.3413

Answer: b) 0.1859

Mean=M = $10,000

Standard deviation =s= $5,000

x1= $12,000

x2= $15,000

z1=(x1-M )/s= 0.4 ...

#### Solution Summary

Answers multiple choice questions on Normal Distribution & Critical Z-Value