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Chapter 10: Q. 20 (page 669)

Final grades for a class are approximately Normally distributed with a mean of 76and a standard deviation of 8. A professor says that the top 10%of the class will receive an A, the next 20%a B, the next 40%a C, the next 20%a D, and the bottom 10%an F. What is the approximate maximum average a student could attain and still receive an F for the course?

(a) 70

(b)69.27

(c) 65.75

(d) 62.84

(e)57

Short Answer

Expert verified

The maximum average a student could attain and still receive an F for the course is 65.75i.e., option (c).

Step by step solution

01

Given Information

We are given that the mean is μ=76and standard deviation is σ=8and we are also given that anything below 10%is considered as an F.

We have to find out the maximum average a student can attain and still receive an F for the course.

02

Explanation

Now using Z score formula as the normal distribution table of mean and standard deviation is not given,

P(Z≤z0)=0.10and then

we will use z0=x0-μσlet this be equation 1....

03

Simplify

Now see the standard table and find the value of Zthat will correspond to 10%.

which gives z0=-1.28

Now put the value in equation 1...

we get -1.28=x0-768

which results x0=65.75

Hence, the maximum average a student could attain is65.75.

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Most popular questions from this chapter

According to sleep researchers, if you are between the ages of 12and 18years old, you need 9hours of sleep to be fully functional. A simple random sample of 28students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was 7.9hours, with a standard deviation of 2.1hours.

Which of the following is the test statistic for the hypothesis test?

(a)t=7.9-92.128

(b)t=9-7.92.128

(c)t=7.9-92.128

(d)t=7.9-92.127

(e)t=9-7.92.127

Do drivers reduce excessive speed when they encounter police radar? Researchers studied the behavior of a sample of drivers on a rural interstate highway in Maryland where the speed limit was 55miles per hour. They measured the speed with an electronic device hidden in the pavement and, to eliminate large trucks, considered only vehicles less than 20feet long. During some time periods (determined at random), police radar was set up at the measurement location. Here are some of the data.

Number of vehiclesNumber over65mphNo radar12,9315,690Radar3,2851,051

(a) The researchers chose a rural highway so that cars would be separated rather than in clusters because some cars might slow when they see other cars slowing. Explain why this is important.

(b) Does the proportion of speeding drivers differ significantly when the radar is being used and when it isn’t? Use information from the Minitab computer output below to support your answer.

“Would you marry a person from a lower social class than your own?” Researchers asked this question of a random sample of 385black, never married students at two historically black colleges in the South. Of the 149men in the sample, 91said “Yes.” Among the 236women, 117said “Yes.”14Is there reason to think that different proportions of men and women in this student population would be willing to marry beneath their class?

Holly carried out the significance test shown below to answer this question. Unfortunately, she made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one.

State: I want to perform a test of

H0:p1=p2

Ha:p1≠p2

at the 95%confidence level.

Plan: If conditions are met, I’ll do a one-sample ztest for comparing two proportions.

  • Random The data came from a random sample of 385 black, never-married students.
  • Normal One student’s answer to the question should have no relationship to another student’s answer.
  • Independent The counts of successes and failures in the two groups—91,58,117, and 119—are all at least 10

Do: From the data, p^1=91149=0.61and p^2=117236=0.46.

Test statistic

z=(0.61-0.46)-00.61(0.39)149+0.46(0.54)236=2.91

p=value From Table A, role="math" localid="1650292307192" P(z≥2.91)≡1-0.3982≡0.0018.

Conclude: The p-value, 0.0018, is less than 0.05, so I’ll reject the null hypothesis. This proves that a higher proportion of men than women are willing to marry someone from a social class lower than their own.

Your teacher brings two bags of colored goldfish crackers to class. She tells you that Bag 1has 25%red crackers and Bag 2has 35%red crackers. Each bag contains more than 500crackers. Using a paper cup, your teacher takes an SRS of 50crackers from Bag 1 and a separate SRS of 40crackers from Bag 2. Let p1^-p2^be the difference in the sample proportions of red crackers.

What is the shape of the sampling distribution ofp1^-p2^ ? Why?

Refer to Exercise 15.

(a) Carry out a significance test at the α=0.05level.

(b) Construct and interpret a 95%confidence interval for the difference between the population proportions. Explain how the confidence interval is consistent with the results of the test in part (a).
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