Question

Use the following information for questions . Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed.

i) Roughly what percentage of regulation basketballs weigh more than 23.1 ounces? Round to the nearest tenth of a percent.

a. Roughly 15.1% of the basketballs will weigh more than 23.1 ounces. b. Roughly 42.3% of the basketballs will weigh more than 23.1 ounces. c. Roughly 36.4% of the basketballs will weigh more than 23.1 ounces. d. Roughly 13.6% of the basketballs will weigh more than 23.1 ounces.

ii) If a regulation basketball is randomly selected, what is the probability that it will weigh between 19.5 and 22.5 ounces? Round to the nearest thousandth.

a. 0.547 b. 0.315 c. 0.685 d. 0.723

Answer 1

This is a normal distribution question with


i) P(x > 23.1)=?
The z-score at x = 23.1 is,

z = 1.1
This implies that
P(x > 23.1) = P(z > 1.1) = 1 - 0.8643339390536173

d. Roughly 13.6% of the basketballs will weigh more than 23.1 ounces.

ii) P(19.5 < x < 22.5)=?

This implies that
P(19.5 < x < 22.5) = P(-2.5 < z < 0.5) = P(Z < 0.5) - P(Z < -2.5)
P(19.5 < x < 22.5) = 0.6914624612740131 - 0.006209665325776132

c. 0.685
PS: you have to refer z score table to find the final probabilities.
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