DSC 423 Final Practice Questions and Answers 2023 with
complete solution
Given z is a random variable from a standard normal population, estimate the
probability using
the 68-95-99.7 Empirical Rule.
P(z <=1 )
84%
Given z is a random variable from a standard normal population, estimate the
probability using
the 68-95-99.7 Empirical Rule.
P(z < -2)
2.5%
Given x is a random variable from a normal population with the indicated mean and
standard deviation, estimate the probability using the 68-95-99.7 Empirical Rule.
P(x < 13 | mean = 15, std = 2)
16%
Given x is a random variable from a normal population with the indicated mean and
standard deviation, estimate the probability using the 68-95-99.7 Empirical Rule.
P(x < 42 | mean = 50, std = 4)
2.5%
Assume the number of miles a car was driven last year is normally distributed with a
mean of 9,000 and a standard deviation of 3,500.
What percent of cars were driven over 15,000 miles last year?
4.32%
Assume the number of miles a car was driven last year is normally distributed with a
mean of 9,000 and a standard deviation of 3,500.
If we define "unusual" as those in the bottom 2.5% or top 2.5%, find the interval for the
"usual" number of miles driven per year.
(2140, 15860)
Assume the number of songs stored on college students' smart phones are normally
distributed with a mean of 500 and a standard deviation of 150.
What percent of students' phones have less than 300 songs?
9.12%
Assume the number of songs stored on college students' smart phones are normally
distributed with a mean of 500 and a standard deviation of 150.
, What is the maximum number of songs a student can have on their smart phone and
still be considered in the bottom 1%?
151
A tire manufacturer claims that the mean life of its tire is 75,000 miles. A sample of 50
tires finds xbar = 74,200 and s = 2300. Test the manufacturer's claim.
Step 1: What is the null hypothesis?
Ho: mu = 75000
Step 2: What is the alternative hypothesis? (Take an adversarial position. Are you
interested in a one-sided or two-sided test?)
Ha: mu < 75000
Step 3: What is the declared alpha?
5% (default)
Step 4: What is z?
-2.46
Step 5: What is the p-value? Remember to consider whether it is a one-tailed or two-
tailed test.
.7%
Step 6: Draw a conclusion.
Reject the null hypothesis and accept the alternative. The manufacture's claims are not
accurate.
A weight loss center claims its participants have a mean loss of 14 pounds in 14 days. A
sample of 100 participants finds x-bar = 13.1 pounds and s = 4.2 pounds. You suspect
they are lying! Test the weight loss center's claim using an alpha of 1%.
Step 1: What is the null hypothesis?
Ho: mu= 14
Step 2: What is the alternative hypothesis? (Take an adversarial position. Are you
interested in a one-sided or two-sided test?)
Ha: mu < 14
Step 3: What is the declared alpha?
1%
Step 4: What is z?
-2.14
Step 5: What is the p-value? Remember to consider whether it is a one-tailed or two-
tailed test.
1.6%
Step 6: Draw a conclusion.
Fail to reject the null hypothesis. The manufacturer's claims may or may not be
accurate. More data is needed.
A supplier claims the mean thickness of its washers is 0.75 inches. Washers that are
too big or too small can cause problems in the machines. A sample of 50 finds xbar =
0.73 inches and s = 0.08 inches. Test the supplier's claim.
Step 1: What is the null hypothesis?
Ho: mu=.75
complete solution
Given z is a random variable from a standard normal population, estimate the
probability using
the 68-95-99.7 Empirical Rule.
P(z <=1 )
84%
Given z is a random variable from a standard normal population, estimate the
probability using
the 68-95-99.7 Empirical Rule.
P(z < -2)
2.5%
Given x is a random variable from a normal population with the indicated mean and
standard deviation, estimate the probability using the 68-95-99.7 Empirical Rule.
P(x < 13 | mean = 15, std = 2)
16%
Given x is a random variable from a normal population with the indicated mean and
standard deviation, estimate the probability using the 68-95-99.7 Empirical Rule.
P(x < 42 | mean = 50, std = 4)
2.5%
Assume the number of miles a car was driven last year is normally distributed with a
mean of 9,000 and a standard deviation of 3,500.
What percent of cars were driven over 15,000 miles last year?
4.32%
Assume the number of miles a car was driven last year is normally distributed with a
mean of 9,000 and a standard deviation of 3,500.
If we define "unusual" as those in the bottom 2.5% or top 2.5%, find the interval for the
"usual" number of miles driven per year.
(2140, 15860)
Assume the number of songs stored on college students' smart phones are normally
distributed with a mean of 500 and a standard deviation of 150.
What percent of students' phones have less than 300 songs?
9.12%
Assume the number of songs stored on college students' smart phones are normally
distributed with a mean of 500 and a standard deviation of 150.
, What is the maximum number of songs a student can have on their smart phone and
still be considered in the bottom 1%?
151
A tire manufacturer claims that the mean life of its tire is 75,000 miles. A sample of 50
tires finds xbar = 74,200 and s = 2300. Test the manufacturer's claim.
Step 1: What is the null hypothesis?
Ho: mu = 75000
Step 2: What is the alternative hypothesis? (Take an adversarial position. Are you
interested in a one-sided or two-sided test?)
Ha: mu < 75000
Step 3: What is the declared alpha?
5% (default)
Step 4: What is z?
-2.46
Step 5: What is the p-value? Remember to consider whether it is a one-tailed or two-
tailed test.
.7%
Step 6: Draw a conclusion.
Reject the null hypothesis and accept the alternative. The manufacture's claims are not
accurate.
A weight loss center claims its participants have a mean loss of 14 pounds in 14 days. A
sample of 100 participants finds x-bar = 13.1 pounds and s = 4.2 pounds. You suspect
they are lying! Test the weight loss center's claim using an alpha of 1%.
Step 1: What is the null hypothesis?
Ho: mu= 14
Step 2: What is the alternative hypothesis? (Take an adversarial position. Are you
interested in a one-sided or two-sided test?)
Ha: mu < 14
Step 3: What is the declared alpha?
1%
Step 4: What is z?
-2.14
Step 5: What is the p-value? Remember to consider whether it is a one-tailed or two-
tailed test.
1.6%
Step 6: Draw a conclusion.
Fail to reject the null hypothesis. The manufacturer's claims may or may not be
accurate. More data is needed.
A supplier claims the mean thickness of its washers is 0.75 inches. Washers that are
too big or too small can cause problems in the machines. A sample of 50 finds xbar =
0.73 inches and s = 0.08 inches. Test the supplier's claim.
Step 1: What is the null hypothesis?
Ho: mu=.75
