Final Examination Questions Fall 2015

Continuous Random Variables

1.

The length of time it takes students to complete a statistics examination is uniformly distributed and varies between

40 and 60 minutes.

a.

b.

c.

d.

e.

Find the mathematical expression for the probability density function.

Compute the probability that a student will take between 45 and 50 minutes to complete the

examination.

Compute the probability that a student will take no more than 40 minutes to complete the

examination.

What is the expected amount of time it takes a student to complete the examination?

What is the variance for the amount of time it takes a student to complete the examination?

ANSWER:

a.

b.

c.

d.

e.

2.

f(x) = 0.05 for 40 ≤ x ≤ 60; zero elsewhere

0.25

0.00

50 minutes

33.33

The advertised weight on a can of soup is 10 ounces. The actual weight in the cans follows a uniform distribution

and varies between 9.3 and 10.3 ounces.

a.

b.

c.

d.

Give the mathematical expression for the probability density function.

What is the probability that a can of soup will have between 9.4 and 10.3 ounces?

What is the mean weight of a can of soup?

What is the standard deviation of the weight?

ANSWER:

a.

b.

c.

d.

3.

f(x) = 1.000 for 9.3

0.90

9.8

0.289

x

10.3; zero elsewhere

The time it takes to completely tune an engine of an automobile follows an exponential distribution with a mean of

40 minutes.

a.

b.

What is the probability of tuning an engine in 30 minutes or less?

What is the probability of tuning an engine between 30 and 35 minutes?

ANSWER:

a.

b.

4.

0.5276

0.0555

The life expectancy of computer terminals is normally distributed with a mean of 4 years and a standard deviation

of 10 months.

a.

b.

c.

d.

What is the probability that a randomly selected terminal will last more than 5 years?

What percentage of terminals will last between 5 and 6 years?

What percentage of terminals will last less...

Continuous Random Variables

1.

The length of time it takes students to complete a statistics examination is uniformly distributed and varies between

40 and 60 minutes.

a.

b.

c.

d.

e.

Find the mathematical expression for the probability density function.

Compute the probability that a student will take between 45 and 50 minutes to complete the

examination.

Compute the probability that a student will take no more than 40 minutes to complete the

examination.

What is the expected amount of time it takes a student to complete the examination?

What is the variance for the amount of time it takes a student to complete the examination?

ANSWER:

a.

b.

c.

d.

e.

2.

f(x) = 0.05 for 40 ≤ x ≤ 60; zero elsewhere

0.25

0.00

50 minutes

33.33

The advertised weight on a can of soup is 10 ounces. The actual weight in the cans follows a uniform distribution

and varies between 9.3 and 10.3 ounces.

a.

b.

c.

d.

Give the mathematical expression for the probability density function.

What is the probability that a can of soup will have between 9.4 and 10.3 ounces?

What is the mean weight of a can of soup?

What is the standard deviation of the weight?

ANSWER:

a.

b.

c.

d.

3.

f(x) = 1.000 for 9.3

0.90

9.8

0.289

x

10.3; zero elsewhere

The time it takes to completely tune an engine of an automobile follows an exponential distribution with a mean of

40 minutes.

a.

b.

What is the probability of tuning an engine in 30 minutes or less?

What is the probability of tuning an engine between 30 and 35 minutes?

ANSWER:

a.

b.

4.

0.5276

0.0555

The life expectancy of computer terminals is normally distributed with a mean of 4 years and a standard deviation

of 10 months.

a.

b.

c.

d.

What is the probability that a randomly selected terminal will last more than 5 years?

What percentage of terminals will last between 5 and 6 years?

What percentage of terminals will last less...