Question

1. Find the area under the standard normal curve between z=0.49 and z=2.05. Round your answer to four decimal places, if necessary.

2. The lengths of nails produced in a factory are normally distributed with a mean of 6.02 centimeters and a standard deviation of 0.05 centimeters. Find the two lengths that separate the top 9% and the bottom 9%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.

______centimeters and ______ centimeters

Answer 1

#1.
Required area = P(0.49 < z < 2.05)
= P(z < 2.05) - P(z < 0.49)
= 0.9798 - 0.6879
= 0.2919

#2.
mean = 6.02 and sd = 0.05
z-value which represents the 0.09 area in either tail of the curve, z = +/- 1.3408

x = (6.02 - 1.3408*0.05, 6.02 + 1.3408*0.05)
= (5.9530, 6.0870)

Ans: 5.9530 cms and 6.0870 cms