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Chapter 7: Q.12 (page 428)

Find the probability that the sum of the 40 values is less than 7,000.

Short Answer

Expert verified

The probability that the sum of the 40 values is less than 7000isP(X鈮�7000)=0.0569.

Step by step solution

01

Given Information

A mean (渭x) is180and a standard deviation (蟽)is 20.

02

Explanation

To find the probability that the sums of the 40values is less than7000:

localid="1649346312817" 鈭�X~Nn渭x,n蟽x

鈭�X~N((40)(180),(40)(20))

localid="1649346327071" P(X鈮�7000)=PZ鈮�X-n渭xn蟽x=PZ鈮�7000-7200126.4911=P(Z鈮�-1.5811)

P(X鈮�7000)=0.0569

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Most popular questions from this chapter

Based on data from the National Health Survey, women between the ages of 18and 24have an average systolic blood pressures (in mm Hg) of 114.8with a standard deviation of 13.1. Systolic blood pressure for women between the ages of 18to 24follow a normal distribution.

a. If one woman from this population is randomly selected, find the probability that her systolic blood pressure is greater than 120.

b. If40women from this population are randomly selected, find the probability that their mean systolic blood pressure is greater than 120.

c. If the sample were four women between the ages of18to 24 and we did not know the original distribution, could the central limit theorem be used?

A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

Find the 90th percentile for the total weight of the 100 weights.

Men have an average weight of 172pounds with a standard deviation of 29pounds.

a. Find the probability that 20randomly selected men will have a sum weight greater than 3600lbs.

b. If 20 men have a sum weight greater than 3500lbs, then their total weight exceeds the safety limits for water taxis. Based on (a), is this a safety concern? Explain.

X~N(60,9). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let 危Xbe the random variable of sums. For parts, c through f, sketch the graph, shade the region, label and scale the horizontal axis for X-, and find the probability.

a. Sketch the distributions of X and X-on the same graph.

b. X-~

c. P(X-<60)=

d. Find the 30th percentile for the mean.

e. P(56<X-<62)

f. P(18<X-<58)=

g. 危齿~

h. Find the minimum value for the upper quartile for the sum.

i. $P(1,400<危齿<1,550)=

Find the percentage of sums between 1.5 standard deviations below the mean and one standard deviation above the mean.
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