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Chapter 7: Q.34 (page 429)

What is the mean of ΣX?

Short Answer

Expert verified

The mean of ∑Xis 10000

Step by step solution

01

Given Information

According to the Given details, the mean of the unknown distribution is 100, the standard deviation is 100 and the sample size is 100 objects of interest.

02

Explanation

Then the mean of ∑Xis given as:

=(n)μX

=100×100

=10000

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Most popular questions from this chapter

The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of \(4.59and a standard deviation of \)0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16gas stations. The distribution to use for the average cost of gasoline for the 16gas stations is:

a.X¯~N(4.59,0.10)

b.X¯~N4.59,0.1016

c.X¯~N4.59,160.10

d.X¯~N4.59,160.10

A uniform distribution has a minimum of six and a maximum of ten. A sample of 50is taken.

Find the first quartile for the sums.

Four friends, Janice, Barbara, Kathy and Roberta, decided to carpool together to get to school. Each day the driver would be chosen by randomly selecting one of the four names. They carpool to school for 96days. Use the normal approximation to the binomial to calculate the following probabilities. Round the standard deviation to four decimal places.

a. Find the probability that Janice is the driver at most20days.

b. Find the probability that Roberta is the driver more than 16days.

c. Find the probability that Barbara drives exactly 24 of those 96 days.

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

Find the middle 80% for the total amount of time 64 batteries last.

M&M candies large candy bags have a claimed net weight of 396.9g. The standard deviation for the weight of the

individual candies is 0.017g. The following table is from a stats experiment conducted by a statistics class.

RedOrangeYellowBrownBlueGreen
0.751
0.735
0.883
0.696
0.881
0.925
0.841
0.895
0.769
0.876
0.863
0.914
0.856
0.865
0.859
0.855
0.775
0.881
0.799
0.864
0.784
0.8060.854
0.865
0.966
0.852
0.824
0.840
0.810
0.865
0.859
0.866
0.858
0.868
0.858
1.015
0.857
0.859
0.848
0.859
0.818
0.876
0.942
0.838
0.851
0.982
0.868
0.809
0.873
0.863


0.803
0.865
0.809
0.888


0.932
0.848
0.890
0.925


0.842
0.940
0.878
0.793


0.832
0.833
0.905
0.977


0.807
0.845

0.850


0.841
0.852

0.830


0.932
0.778

0.856


0.833
0.814

0.842


0.881
0.791

0.778


0.818
0.810

0.786


0.864
0.881

0.853


0.825


0.864


0.855


0.873


0.942


0.880


0.825


0.882


0.869


0.931


0.912





0.887

The bag contained 465candies and the listed weights in the table came from randomly selected candies. Count the weights.

a. Find the mean sample weight and the standard deviation of the sample weights of candies in the table.

b. Find the sum of the sample weights in the table and the standard deviation of the sum of the weights.

c. If 465M&Ms are randomly selected, find the probability that their weights sum to at least 396.9.

d. Is the Mars Company’s M&M labeling accurate?
See all solutions

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