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Chapter 6: Q.15 (page 355)

Spell-checking Refer to Exercise 3. Calculate and interpret the standard deviation of the random variable X. Show your work

Short Answer

Expert verified

The number of nonword errors is on average 1.1358 words from the mean.

Step by step solution

01

Given Information

The distribution of the number Xof nonword errors is as follows:

02

Explanation

The expected value is calculated by multiplying each possibility by its probability:

E(X)=∑xP(x)=0×0.1+1×0.2+2×0.3+3×0.3+4×0.1=2.1

The expected value of the squared variation from the mean is the variance:

σ2=∑(x-μ)2P(x)=(0-2.1)2×0.1+(1-2.1)2×0.2+(2-2.1)2×0.3+(3-2.1)2×0.3+(4-2.1)2×0.1=1.29

The square root of the variance is the standard deviation:

σ=σ2=1.29≈1.1358

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Most popular questions from this chapter

The mean of Tis

(a)110

(b)140

(c)180

(d)195

(e)250

Kids and toys Refer to Exercise 4. Calculate the mean of the random variable X and interpret this result in context.

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 T=X+Y.

Find and interpret μT.

18. Life insurance

(a) It would be quite risky for you to insure the life of a 21-year-old friend under the terms of Exercise 14. There is a high probability that your friend would live and you would gain \(1250in premiums. But if he were to die, you would lose almost \)100,000. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21-year-old men.

(b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the
investment. We can measure the great risk of insuring a single person’s life in Exercise 14by computing the standard deviation of the income Y that the insurer will receive. Find σY using the distribution and mean found in Exercise 14.

Toss 4times Suppose you toss a fair coin 4times. Let X=the number of heads you get.

(a) Find the probability distribution ofX.

(b) Make a histogram of the probability distribution. Describe what you see.

(c) Find P(X≤3) and interpret the result.
See all solutions

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