Question

Courses 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. If a regulation basketball is randomly selected, what is the probability that will weigh between 19.5 and 22.5 ounces? urse Hom mework O A. 0.723 OB. 0.315 OC. 0.685 OD. 0.547 uizzes & T udy Plan Facebook

Answer 1

Solution-

The probability that the weight between 19.5 and 22.5 onces is -

● C. 0.685

Option C is correct.

◆ Probability calculation-

The following information has been provided: M = 22.0, 0 = 1.0 We need to compute Pr(19.5 < X < 22.5). The corresponding z-values needed to be computed are: X μ 21 19.5 – 22.0 1.0 = -2.5 o X2 – u 22 22.5 – 22.0 1.0 = 0.5 0 Therefore, we get: Pr(19.5 < X < 22.5) = Pr 19.5 – 22.0 1.0 <2< 22.5 – 22.0 1.0 22.0) = Pr(–2.5 < 3 < 0.5) = Pr(Z < 0.5) – Pr(Z < -2.5) = 0.6915 – 0.0062 = 0.6853 The following is obtained graphically: Normal Distribution: Pr(19.5<X<22.5)=0.6853 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0

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