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Chapter 7: Q. 72 (page 481)

Lightning strikes The number of lightning strikes on a square kilometer of open ground in a year has mean 6 and standard deviation 2.4. The National Lightning Detection Network (NLDN) uses automatic sensors to watch for lightning in 1-square-kilometer plots of land. Find the probability that the total number of lightning strikes in a random sample of 50 square-kilometer plots of land is less than 250.

Short Answer

Expert verified

The resultant value isP(X炉<5)=0.0016

Step by step solution

01

Given information 

Given:

mu=6蟽=2.4n=50鈭�xi=250

Formula used:

z=x-渭蟽
02

Calculation

Simplify

x炉=鈭�xin=25050=5z=x炉-渭x炉蟽x炉=x炉-渭蟽/n=5-62.4/50鈮�-2.95z=x炉-渭x炉蟽x炉=x炉-渭蟽/n=5-62.4/50鈮�-2.95P(X炉<5)=P(Z<-2.95)=0.0016=0.16%

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Most popular questions from this chapter

A newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was x-x炉=810grams. This sample mean is an unbiased estimator of the mean weight 渭 in the population of all ELBW babies, which means that

a. in all possible samples of size 219 from this population, the mean of the values of x-x炉will equal 810 .

b. in all possible samples of size 219 from this population, the mean of the values of x-x炉will equal 渭

c. as we take larger and larger samples from this population, x-x炉will get closer and closer to 渭.

d. in all possible samples of size 219 from this population, the values of x-x炉will have a distribution that is close to Normal.

e. the person measuring the children's weights does so without any error.

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identify the population, the parameter, the sample, and the statistic.
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