Problem 1: The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is: Between the mean and $45 per hour? More than $45 per hour? Less than $32 per hour? Problem 2: The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of randomly selecting a value less than 395 pounds? Problem 3: In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution. What percent of New York State high school teachers earn between 70,000 and 75,000? What percent of New York State high school teachers earn between 75,000 and 90,000? What percent of New York State high school teachers earn less than $60,000? Problem 4: Among the 30 largest US cities, the mean one-way commute time to work is 25.8 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution, and the standard deviation is 7.5 minutes. What percent of New York City commuters travel for less than 30 minutes? What percent travel between 30 and 35 minutes? What percent travel between 30 and 50 minutes?

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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Problem 1:

The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is:

Between the mean and $45 per hour?
More than $45 per hour?
Less than $32 per hour?

Problem 2:

The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds.

What is the area between 415 pounds and the mean of 400 pounds?
What is the area between the mean and 395 pounds?
What is the probability of randomly selecting a value less than 395 pounds?

Problem 3:

In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution.

What percent of New York State high school teachers earn between 70,000 and 75,000?
What percent of New York State high school teachers earn between 75,000 and 90,000?
What percent of New York State high school teachers earn less than $60,000?

Problem 4:

Among the 30 largest US cities, the mean one-way commute time to work is 25.8 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution, and the standard deviation is 7.5 minutes.

What percent of New York City commuters travel for less than 30 minutes?
What percent travel between 30 and 35 minutes?
What percent travel between 30 and 50 minutes?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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