A new gas-electric hybrid car has recently hit the market....

Name: Problem 44, Chapter 8: Statistics for Management and Economics
Uploaded: 2021-09-22T02:13:12-08:00
Duration: 2 min 24 s
Channel: Sneha Ravi
Description: A new gas-electric hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find the probability of the following events. a. The car travels more than 70 miles per gallon. b. The car travels less than 60 miles per gallon. c. The car travels between 55 and 70 miles per gallon.

A new gas-electric hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find the probability of the following events. a. The car travels more than 70 miles per gallon. b. The car travels less than 60 miles per gallon. c. The car travels between 55 and 70 miles per gallon.

A new gas-electric hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find the probability of the following events.
a. The car travels more than 70 miles per gallon.
b. The car travels less than 60 miles per gallon.
c. The car travels between 55 and 70 miles per gallon.

Key Concepts

Mean and Standard Deviation

The mean is the average value of a data set and serves as the center of the normal distribution. The standard deviation quantifies the amount of variation or dispersion around the mean. Together, these parameters fully describe the behavior and shape of a normally distributed variable.

Z-Score Transformation

A z-score transformation converts a value from a normal distribution into a standard score, which represents the number of standard deviations that value is from the mean. This standardization process allows for the comparison of values from different normal distributions and facilitates the use of standard normal distribution tables to find probabilities.

Normal Distribution

The normal distribution is a common continuous probability distribution characterized by a bell-shaped curve that is symmetric about its mean. It is used to model many real-world phenomena, and its key parameters are the mean (which indicates the central location) and the standard deviation (which reflects the spread or dispersion of the data).

Cumulative Distribution Function (CDF)

The cumulative distribution function (CDF) of a normal distribution gives the probability that a random variable will take a value less than or equal to a specific value. By using the CDF and its complement, one can compute the probabilities for various events, such as being above or below a certain threshold or falling within a given interval.

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