Answered: In the public schools in Massachusetts,…

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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Question

In the public schools in Massachusetts, the average number of students per computer for the 2007–2008 school year was 3.6 with a standard deviation of 1.3. A random sample of 30 public schools in the state of Massachusetts was obtained last year, and the average number of students per computer was found to be 4.2.

Determine the mean (in students per computer) of the sampling distribution of the sample mean.

students per computer

(b)

Calculate the standard deviation (in students per computer) of the sampling distribution of the sample mean. (Round your answer to three decimal places.)

students per computer

(c)

The shape of the sampling distribution of the sample mean is approximately normal. Which of the following choices justifies that statement?

We have sampled less than 10% of the population.The population is approximately normally distributed. The sample size is 30 or more.A random sample was taken.

(d)

What is the probability of obtaining a sample average of 4.2 students per computer or more if the average number of students per computer has not changed since the 2007–2008 school year? (Use a table or technology. Round your answer to four decimal places.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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