6.2 Using the Normal Distribution
Areas to the left of a value turned into probabilities, working backwards from a given area to the cutoff, and locating percentiles on a bell curve.
Introductory Statistics 2e, 6.2 Using the Normal Distribution
19 exercises
6.2 Exercise 3
b. Find the probability that a randomly selected student scored less than 85.
6.2 Exercise 5
d. Find the 70th percentile (that is, find the score k such that 70% of scores are below k and 30% of the scores are above k).
6.2 Exercise 10
In the United States the ages 13 to 55+ of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 36.9 years and 13.9 years, respectively.
a. Determine the probability that a random smartphone user in the age range 13 to 55+ is between 23 and 64.7 years old.
b. Determine the probability that a randomly selected smartphone user in the age range 1…
6.2 Exercise 12
In the United States the ages 13 to 55+ of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 36.9 years and 13.9 years respectively. Using this information, answer the following questions (round answers to one decimal place).
a. Calculate the interquartile range (IQR).
b. Forty percent of the smartphone users from 13 to 55+ are at least wha…
6.2 Exercise 18
Is P(x < 1) equal to P(x ≤ 1)? Why?
6.2 Exercise 22
If the area to the right of x in a normal distribution is 0.543, what is the area to the left of x?
6.2 Exercise 24
X ~ N(54, 8)
Find the probability that x < 30.
6.2 Exercise 26
X ~ N(54, 8)
Find the 60th percentile.
6.2 Exercise 28
X ~ N(54, 8)
X ~ N(–3, 4)
Find the probability that x is between one and four.
6.2 Exercise 34
Use the following information to answer the next two exercises: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.
The 90th percentile for recovery times is?
- 8.89
- 7.07
- 7.99
- 4.32
6.2 Exercise 36
Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
Find the probability that it takes at least eight minutes to find a parking space.
- 0.0001
- 0.9270
- 0.1862
- 0.0668
6.2 Exercise 38
Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches.…
6.2 Exercise 40
Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one indi…
6.2 Exercise 42
Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
In China, four-year-olds average three hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviatio…
6.2 Exercise 44
Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days.
- In words…
6.2 Exercise 46
Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
Thuy Dau, Ngoc Bui, Sam Su, and Lan Voung conducted a survey as to how long customers at Lucky claimed to wait in the checkout line until their turn. Let X = time in line. t…
6.2 Exercise 48
Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
the table shows a sample of the maximum capacity (maximum number of spectators) of sports stadiums. The table does not include horse-racing or motor-racing stadiums.
- Calc…
6.2 Exercise 50
Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
An automotive factory can build an average of 6,000 cars and trucks a week. Generally, 10% of the cars were defective coming off the assembly line. Suppose we draw a random…
6.2 Exercise 52
Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
A $1 scratch off lotto ticket will be a winner one out of five times. Out of a shipment of n = 190 lotto tickets, find the probability for the lotto tickets that there are
- …
Adapted from Introductory Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Statistics 2e. Imported at revision 50ec917.