Salaries of a city follows a normal distribution with average salary of $1 million. Assume that salary is normally distributed. Suppose a sample of 60 citizens was taken. The sample standard deviation is $0.1 million. (a) What is the standard error for the sample mean salary? (b) What is the probability that the sample mean salary is more than $1.2 million? (c) What is the probability that the sample mean salary is less than $1.4 million? (d) What is the probability that the sample mean salary is between than $1.1 million and $1.3 million?

Salaries of a city follows a normal distribution with average salary of $1 million. Assume that salary is normally distributed. Suppose a sample of 60 citizens was taken. The sample standard deviation is $0.1 million. (a) What is the standard error for the sample mean salary? (b) What is the probability that the sample mean salary is more than $1.2 million? (c) What is the probability that the sample mean salary is less than $1.4 million? (d) What is the probability that the sample mean salary is between than $1.1 million and $1.3 million?

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

Q2. (Sample mean with unknown population variance) Salaries of a city follows a normal distribution with average salary of $1 million. Assume that salary is normally distributed. Suppose a sample of 60 citizens was taken. The sample standard deviation is $0.1 million.

(a) What is the standard error for the sample mean salary?

(b) What is the probability that the sample mean salary is more than $1.2 million?

(d) What is the probability that the sample mean salary is between than $1.1 million

and $1.3 million?

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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