Internet hookup, insurance spending, 3 songs, home loans
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1. Customers experiencing technical difficulties with their internet cable hook up may call 800 numbers for technical support. It takes the technician between 30 second to 10 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.
a. what are the values for a and b in minutes?
b. what is the mean time to resolve the problem? What is the standard deviation of the time?
c. what percent of the problem take more than 5 minutes to resolve
d suppose we which to find the middle of 50 % of the problem solving-times. What are the end points of these two times?
2. According to the insurance institute of America, families of four spend between $400 and $3800 per person in all type of insurance. Suppose the money spend is uniformly distributed between these amounts,
a. what is the mean of money spend in insurance?
b. what is the standard deviation of the amount spent?
c. if we selected a family at random, what is the probability they spend less that $2000 per year on insurance per year?
d. what is the probability a family spend more than $3000 per year?
3. . You are asking to match three songs with the performers who made those songs famous. If you guess, the probability distribution for the number of correct matches is:
What is the probability you get
a. Exactly one correct?
b. At least one correct?
c. Exactly two correct?
d. Compute the mean, variance, and standard deviation of this distribution
4. Refer to exercise 20, where the amount requested for home loans followed the normal distribution which a mean of 70,000 and the standard deviation of 20,000.
a. how much is requested on the largest 3 % of the loans?
b. how much is requested on the smallest 10 percent of the loans?
5. Past surveys reveal that 30 percent of tourist going to Las Vegas to gamble during the weekend spends more than $1,000. The Las Vegas area chamber of commerce wants to update this percentage.
a. the new study is to use the 90 percent confidence level. This estimate is to be within 1 % of population proportion. What is the necessary sample size?
b. Management said that the sample size determined above is too large. What can be done to reduce the sample? Based on your suggestion recalculate the sample size
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Solution Summary
The expert examines internet hookups, insurance spending, three songs and home loans.
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1. Suppose X denotes the support time. Given X follows uniform distribution in the interval 30 second (0.5 minutes) to 10 minutes. Symbolically, . Hence the probability density function of X is given by
For a uniform distribution Mean = , Median = and Variance =
a) Here a = 0.5 and b = 10
b) Mean time to resolve the problem = ;
Standard deviation =
c) Probability that it take more than 5 minutes to resolve a problem is .
Percentage of problems that take more than 5 minutes to resolve = 52.63%
d) Middle of problem solving time is Median = 5.25. Hence the end points of these two times is : First Half 0.5 minutes to 5.25 minutes; Second half 5.25 minutes to 10 minutes
2. Let X denotes the money spend for insurance. Given X follows uniform distribution in the interval $400 and $3800. Symbolically, . Hence the probability density function of X is given by
For a uniform distribution Mean = and Variance = ...
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