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Chapter 6: Q.71 (page 403)

Explain whether the given random variable has a binomial distribution.

Lefties Exactly 10%of the students in a school are left-handed. Select students at random from the school, one at a time, until you find one who is left-handed. Let V=the number of students chosen.

Short Answer

Expert verified

The given distribution is not binomial

Step by step solution

01

Given Explanation

Exactly 10%of the students in a school are left-handed.

We have to find students one who is left-handed at random from the school.

02

Explanation

The variable Vin this question is not a binomial distribution because each subsequent draw is dependent on the preceding draw because there is no fixed amount of pieces drawn each time. Only after a left-handed person is found is the draw made.

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Most popular questions from this chapter

The mean of Tis

(a)110

(b)140

(c)180

(d)195

(e)250

Exercises 47 and 48 refer to the following setting. Two independent random variables Xand Yhave the probability distributions, means, and standard deviations shown.

48. Difference Let the random variable D=X-Y.

(a) Find all possible values of D. Compute the probability that Dtakes each of these values. Summarize the probability distribution ofD in a table.
(b) Show that the mean of Dis equal toμX-μY.
(c) Confirm that the variance of Dis equal to σX2+σY2.Find all possible values of D. Compute the probability that takes each of these values. Summarize the probability distribution of in a table.

45. Too cool at the cabin? During the winter months, the temperatures at the Stameses' Colorado cabin can stay well below freezing 32°For 0°Cfor weeks at a time. To prevent the pipes from freezing, Mrs. Stames sets the thermostat at 50°F. She also buys a digital thermometer that records the indoor temperature each night at midnight. Unfortunately, the thermometer is programmed to measure the temperature in degrees Celsius. Based on several years' worth of data, the temperature Tin the cabin at midnight on a randomly selected night follows a Normal distribution with mean 8.5°Cand standard deviation2.25°C.
(a) Let Y=the temperature in the cabin at midnight on a randomly selected night in degrees Fahrenheit (recall that F=(9/5)C+32). Find the mean and standard deviation of Y.

(b) Find the probability that the midnight temperature in the cabin is below 40°F. Show your work.

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)?

83. Random digit dialing Refer to Exercise 81. Let Y= the number of calls that don’t reach a live person.

(a) Find the mean of Y. How is it related to the mean of X? Explain why this makes sense.
(b) Find the standard deviation of Y.How is it related to the standard deviation of X? Explain why this makes sense

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