3.) a.) Many cylinders are to be produced for a laboratory application. Suppose

Question

3.)
a.) Many cylinders are to be produced for a laboratory application. Suppose that the thickness of a cylinder has a normal distribution with a mean of 1.41 cm and a standard deviation of 0.01 cm. What is the probability that the thickness is greater than 1.42 cm?
b.) The grades on a statistics exam follow a normal distribution with a mean of 65 and a standard deviation of 12. Approximately what percentage of the students have scores below 50?


4.) Suppose that a given basketball player is a 70% free-throw shooter.
a.) What is the probability that he makes his first free throw on his fourth shot?
b.) What is the probability that he makes his third free throw on his fifth shot?

Explanation / Answer

3. a) we are given = 1.41, = 0.01

z(x=1.42) = (1.42-1.41)/0.01 = 1

z-score = 0.8413

probability (thickness > 1.42) = 1-0.8413 = 0.1587

b) = 65, = 12

z (x =50) = (50-65)/12 = -1.25

z-score = 0.1056

probability of scores below 50 = 0.1056

4) a)he missed his shot in first, 2nd, and 3rd throw, each with probability of (1- 0.70)

P = (1-0.70)3 (0.70) = 0.0189

b) he made 2 shots in first 4 throws,

there are C(4,2) ways to make those 2 shots in the first 4 throws

P = C(4,2)(1-0.7)2*(0.7)2 *(0.7) = 6*(0.3)2(0.7)3 = 0.185

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