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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¯<5)=0.0016

Step by step solution

01

Given information 

Given:

mu=6σ=2.4n=50∑xi=250

Formula used:

z=x-μσ
02

Calculation

Simplify

x¯=∑xin=25050=5z=x¯-μx¯σx¯=x¯-μσ/n=5-62.4/50≈-2.95z=x¯-μx¯σx¯=x¯-μσ/n=5-62.4/50≈-2.95P(X¯<5)=P(Z<-2.95)=0.0016=0.16%

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Most popular questions from this chapter

A statistic is an unbiased estimator of a parameter when

a. the statistic is calculated from a random sample.

b. in a single sample, the value of the statistic is equal to the value of the parameter.

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e. in many samples, the distribution of the statistic has a shape that is approximately

Normal.

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b. What is the probability that the mean contents of six randomly selected bottles is less than 295ml?

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a. Sketch a graph that displays the distribution of birth weights for this population.

b. Sketch a possible graph of the distribution of birth weights for an SRS of size $5 . Calculate the range for this sample.

In this population, the range (Maximum - Minimum) of birth weights is 3417 grams. We technology to take 500 SRSs of size n=5n=5and calculate the range (Maximum Minimum) for each sample. The dotplot shows the results.

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a. Identify the mean of the sampling distribution of x-x¯.

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According to government data, 22%of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in

early childhood chooses an SRS of300 children from one state and finds that p∧p^=.

a. Find the probability that at least 29%of the sample are from poverty-level households0.29households.

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