A recent report by the MLB shows that a typical family of four spends $490 to watch a professional game. Assume the distribution of attending a game in person follows the normal distribution with a mean of $490 and a standard deviation of $30. 1) What is the probability that a randomly selected family of four spends less than $430 to watch a game in person? 2) What is the probability that a randomly selected family of four spends more than $430 to watch a game in person? 3) What is the probability that a randomly selected family of four spends between $430 and $550 to watch a game in person?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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A recent report by the MLB shows that a typical family of four spends $490 to watch a professional game. Assume the distribution of attending a game in person follows the normal distribution with a mean of $490 and a standard deviation of $30.

1) What is the probability that a randomly selected family of four spends less than $430 to watch a game in person?

2) What is the probability that a randomly selected family of four spends more than $430 to watch a game in person?

3) What is the probability that a randomly selected family of four spends between $430 and $550 to watch a game in person?

Expert Solution
Step 1

Given Information:

Let the random variable X denotes the attending a game in person.

X has normal distribution with a mean of $490 and a standard deviation of $30.

Hence,

Statistics homework question answer, step 1, image 1

Step 2

1)

The probability that a randomly selected family of four spends less than $430 to watch a game in person can be obtained as:

Statistics homework question answer, step 2, image 1

The z-value is obtained using the statistical tables.

Therefore, the probability that a randomly selected family of four spends less than $430 to watch a game in person is 0.0228.

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