A random sample of 100 observations is obtained from a normally distributed population with a standard deviation of 10

Problem 1

Problem 2

Problem 3

1. Find the probability that a normal standard variable is less than or equal 0.

2. Given a normal distribution with  = 3 and  = 0.5, find the probability that X assumes

a value less than or equal 2.3.

Problem 4

9 friends decide to  “go  for  a  drink”   after an exam. What is the probability that the waitress will refuse to serve alcoholic beverages to only 2 minors if she randomly checks the IDs of 5 students from among 9 students of which 4 are not of legal age?

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MGM 5700 Probability and Statistical Methods Take-home Problems #2 Summer 2013 Problem 1 (25 points) 1. A random sample of 100 recorded deaths in the United States during the past year showed an

average life span of 71.8 years, with a standard deviation of 8.9 years. Does this seem to indicate that

the mean life span today is greater than 70 years? Use a 0.05 level of significance.

2. Calculate the 90% confidence interval for the average life span.

Problem 2 (25 points)

Independent random samples of 45 and 55 soft drinks are drawn from two soft-drink machines. Sample

average content and standard deviation were obtained for both samples. The sample data is presented

in the following table:

Machine 1 Machine 2

Sample size

Sample mean

45

11.84 oz

55

11.91 oz

Sample stand. dev. 0.046 oz 0.044 oz

Do the data present sufficient evidence to indicate that the mean for the machine 1 is smaller than the

mean for the machine 2? Use a 0.05 level of significance.

MGM 5700 Probability and Statistical Methods Take-home Problems #2 Summer 2013 Problem 1 (25 points) 1. A random sample of 100 recorded deaths in the United States during the past year showed an average life span of 71.8 years, with a standard deviation of 8.9 years. Does this seem to indicate that the mean life span today is greater than 70 years? Use a 0.05 level of significance. 2. Calculate the 90% confidence interval for the average life span.

Problem 2 (25 points)

Independent random samples of 45 and 55 soft drinks are drawn from two soft-drink machines. Sample

average content and standard deviation were obtained for both samples. The sample data is presented

in the following table:

Machine 1 Machine 2

Sample size

Sample mean

45

11.84 oz

55

11.91 oz

Sample stand. dev. 0.046 oz 0.044 oz

Do the data present sufficient evidence to indicate that the mean for the machine 1 is smaller than the

mean for the machine 2? Use a 0.05 level of significance.

MGM 5700 Probability and Statistical Methods Take-home Problems #2 Summer 2013 Problem 1 (25 points) 1. A random sample of 100 recorded deaths in the United States during the past year showed an average life span of 71.8 years, with a standard deviation of 8.9 years. Does this seem to indicate that the mean life span today is greater than 70 years? Use a 0.05 level of significance. 2. Calculate the 90% confidence interval for the average life span. Problem 2 (25 points) Independent random samples of 45 and 55 soft drinks are drawn from two soft-drink machines. Sample

average content and standard deviation were obtained for both samples. The sample data is presented

in the following table:

Machine 1 Machine 2

Sample size

Sample mean

45

11.84 oz

55

11.91 oz

Sample stand. dev. 0.046 oz 0.044 oz

Do the data present sufficient evidence to indicate that the mean for the machine 1 is smaller than the

mean for the machine 2? Use a 0.05 level of significance.