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Chapter 6: Q.2.1 (page 349)

A large auto dealership keeps track of sales made during each hour of the day. Let X=the number of cars sold during the first hour of business on a randomly selected Friday. Based on previous records, the probability distribution of Xis as follows:

Compute and interpret the mean of X.

Short Answer

Expert verified

The mean of Xis 8.128.

Step by step solution

01

Given information

Given in the question that, A large auto dealership keeps track of sales made during each hour of the day. Let X= the number of cars sold during the first hour of business on a randomly selected Friday. Based on previous records, the probability distribution of Xis as follows:

We need to compute the mean of X.

02

Explanation

The probability distribution is following

X
0
1
2
3
4
5
6
7
8
10
P(X)
0.001
0.006
0.007
0.008
0.012
0.02
0.038
0.099
0.319
0.053

The formulas to compute the mean is:

Mean=∑x×P(x)

The mean can be calculated as:

Mean=∑x×P(x)=0(0.001)+1(0.006)+….+10(0.053)=0+0.006+…..+0.53=8.128

After one minute, an Apgar score of8.128is expected for a randomly picked infant.

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Most popular questions from this chapter

Benford’s law and fraud A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts should be equally likely to be any of the numbers from 1to 9. In that case, the first digit Yof a randomly selected expense amount would have the probability distribution shown in the histogram.

(a). Explain why the mean of the random variable Y is located at the solid red line in the figure.

(b) The first digits of randomly selected expense amounts actually follow Benford’s law (Exercise 5). What’s the expected value of the first digit? Explain how this information could be used to detect a fake expense report.

(c) What’s P(Y>6)? According to Benford’s law, what proportion of first digits in the employee’s expense amounts should be greater than 6? How could this information be used to detect a fake expense report?

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the first hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

Define D=X-Y.

The dealership’s manager receives a 500bonus for each car sold and a300 bonus for each car leased. Find the mean and standard deviation of the difference in the manager’s bonus for cars sold and leased. Show your work.

Buying stock (5.3,6.1)You purchase a hot stock for 1000. The stock either gains 30%or loses 25%each day, each with probability 0.5. Its returns on consecutive days are independent of each other. You plan to sell the stock after two days.

(a) What are the possible values of the stock after two days, and what is the probability for each value? What is the probability that the stock is worth more after two days than the 1000you paid for it?

(b) What is the mean value of the stock after two days?

(Comment: You see that these two criteria give different answers to the question "Should I invest?")

Days01234567Probability0.680.050.070.080.050.040.010.02

Working out Refer to Exercise 6. Consider the events A = works out at least once and B = works out less than 5 times per week.

(a) What outcomes makeup event A? What is P(A)?

(b) What outcomes make up event B? What is P(B)?

(c) What outcomes make up the event “A and B”? What is P(A and B)? Why is this probability not equal to P(A) · P(B)?

A report of the National Center for Health Statistics says that the height of a 20-year-old man chosen at random is a random variable H with mean 5.8feet (ft) and standard deviation0.24 ft. Find the mean and standard deviation of the height J of a randomly selected 20-year-old man in inches. There are 12 inches in a foot
See all solutions

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