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

Answer:

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

Step-by-step 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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

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

$P(100 \leq x \leq 110) = P(\displaystyle\frac{100 - 105}{11} \leq z \leq \displaystyle\frac{110-105}{11}) = P(-0.454 \leq z \leq 0.454)\\\\= P(z \leq 0.454) - P(z < -0.454)\\= 0.675 - 0.325 = 0.35$

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

$P(100 \leq x \leq 110) = P(\displaystyle\frac{100 - 95}{11} \leq z \leq \displaystyle\frac{110-95}{11}) = P(0.454 \leq z \leq 1.363)\\\\= P(z \leq 1.363) - P(z < 0.454)\\= 0.914 - 0.675 = 0.239$

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