Question

4. In Problem 2, you were told that the durations of high school baseball games are approximately normally distributed with a mean of 105 minutes and a standard deviation of 11 minutes.

Suppose also that the durations of high school softball games are approximately normally distributed with a mean of 95 minutes and the same standard deviation, 11 minutes. Is it more
likely that a high school baseball game will last between 100 and 110 minutes or that a high school softball game will last between 100 and 110 minutes? Answer this question without
doing any calculations.

Answer 1

It is more likely that a high school baseball game will last between 100 and 110 minutes or that a high school softball game will last between 100 and 110 minutes

Explanation:

We are given the following information in the question:

Basket ball game:

Mean, μ = 105 minutes

Standard Deviation, σ = 11 minutes

Softball game:

Mean, μ = 95 minutes

Standard Deviation, σ = 11 minutes

We are given that the distribution of durations of high school baseball games is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(basketball game will last between 100 and 110 minutes)

`P(100 \leq x \leq 110) = P(\displaystyle(100 - 105)/(11) \leq z \leq \displaystyle(110-105)/(11)) = P(-0.454 \leq z \leq 0.454)\\\\= P(z \leq 0.454) - P(z < -0.454)\\= 0.675 - 0.325 = 0.35`

P(softball game will last between 100 and 110 minutes)

`P(100 \leq x \leq 110) = P(\displaystyle(100 - 95)/(11) \leq z \leq \displaystyle(110-95)/(11)) = P(0.454 \leq z \leq 1.363)\\\\= P(z \leq 1.363) - P(z < 0.454)\\= 0.914 - 0.675 = 0.239`

Since,

P(basketball game) > P(softball game)

It is more likely that a high school baseball game will last between 100 and 110 minutes or that a high school softball game will last between 100 and 110 minutes