One season, the average little league baseball game averaged 2 hours and 48 minutes (168 minutes) to complete. Assume the length of games follows the normal distribution with a standard deviation of
10 minutes. Complete parts a through d below.
a. What is the probability that a randomly selected game will be completed in less than 170 minutes?
(Round to four decimal places as needed.)
b. What is the probability that a randomly selected game will be completed in more than 170 minutes?
(Round to four decimal places as needed.)
c. What is the probability that a randomly selected game will be completed in exactly 170 minutes?
(Round to four decimal places as needed.)
d. What is the completion time in which 99% of the games will be finished?
(Round to two decimal places as needed.)

The answers are as follows

(a)  0.5793

(b) 0.4207

(c) 0.5793

(d) 177.9 minutes.

Explanation:

Given,

Average = 168 minutes. Average is called as mean.

So, mean(m) = 168

standard deviation(sd) = 10

Using the formula, Z = (X - m)/(sd)

(a) here X = 170

so, Z = (170 - 168)/(10) => 2/10 => 0.2

It was asked to find the probability that a randomly selected game will be completed in less than 170 minutes.

it implies X < 170 => Z < 0.2

P(X < 170) = P(Z < 0.2) = 0.5793 from Z table.

(b) here X = 170

so, Z = (170 - 168)/(10) => 2/10 => 0.2

It was asked to find the probability that a randomly selected game will be completed in more than 170 minutes.

it implies X > 170 => Z > 0.2

P(X > 170) = P(Z > 0.2) = 1 - 0.5793 = 0.4207 from Z table.

(c) here X = 170

so, Z = (170 - 168)/(10) => 2/10 => 0.2

It was asked to find the probability that a randomly selected game will be completed in less than 170 minutes.

it implies X = 170 => Z = 0.2

P(X = 170) = P(Z = 0.2) = 0.5793 from Z table.

(d) Here Probability = 99% = 0.99

P(Z) = 0.99

Substituting the values in Z = (X - m)/(sd) and finding X

0.99 = (X - 168)/(10) => 9.9 = (X - 168) => X = 177.9

Therefore, the completion time in which 99% of the games will be finished is 177.9 minutes.

cash flow statement possibly

d. automatic stabilizers.

explanation: