Question

1) A machine is designed to produce bolts with a 3-in diameter. The actual diameter of the bolts has a normal distribution with mean of 3.002 in and standard deviation of 0.002 in. Each bolt is measured and accepted if the length is within 0.005 in of 3 in; otherwise the bolt is scrapped. Find the percentage of bolts that are scrapped.

		6.68%
		93.32%
		3.34%
		50%

2)

1. A random variable X is normally distributed with a mean of 100. If P(X > 90) = 0.8413, then the standard deviation of X is

   		5
   		10
   		15
   		20

2. The systolic blood pressure of adults are approximately normally distributed with a mean of 128 and a standard deviation of 20. Give an interval in which the blood pressures of 68.26% of the population will fall.

   		88 to 168
   		68 to 188
   		108 to 148
   		88 to 188

Answer 1

(1)

μ = 3.002, σ = 0.002, x1 = 3 - 0.005 = 2.995, x2 = 3 + 0.005 = 3.005

z1 = (x - μ)/σ =(2.995 - 3.002)/0.002 = -3.5 and z2 = (x2 - μ)/σ = (3.005 - 3.002)/0.002 = 1.5

P(x < 2.995 or x > 3.005) = 0.067 (6.7%)

Answer: Option (a)

(2)

The right-tail z- score for 0.8413 is -1

(90 - 100)/σ = -1

Upon solving, we get σ = 10

Option (b)

(3)

68.26% corresponds to 1 standard deviation of the mean

x1 = 128 - 1 * 20 = 108, x2 = 128 + 1 * 20 = 148

The interval is [108, 148]

Option (c)