MAT 202 FINAL PAPER 2025/2026 QUESTIONS WITH
ANSWERS TAGGED A+
✔✔Carter Motor Company claims that its new sedan, the Libra, will average better than
30 miles per gallon in the city. Use μ, the true average mileage of the Libra, express the
null hypothesis H0 and the alternative hypothesis H1 in symbolic form.
(i) H0: μ = 30; H1: μ < 30
(ii) H0: μ < 30; H1: μ ≥30
(iii) H0: μ = 30; H1: μ > 30
(iv) H0: μ > 30; H1: μ ≤30 - ✔✔C. (iii)
✔✔The scores of a final exam in Math are normally distributed with mean of 73 with
standard deviation 78. If 24 students are randomly selected, find the probability that the
mean of their test scores in greater than 78
Let P(Z <314)-0.9992. PIZ-1.26)-0.8962 - ✔✔B 0.0008
✔✔Use the margin of error.
confidence level, and standard deviation to find the minimum sample size required to
estimate an unknown population mean.
Margin of error: $126. confidence level: 99%, standard deviation = $534.
Let z0.005 = 2.58 - ✔✔B. 120
✔✔The volumes of soda in quart soda bottles are normally distributed with a mean of
32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of
soda in a randomly selected bottle will be less than 32 oz?
Let P(Z < 0.25) = 0.5987, P(Z < -0.3) = 0.3821. - ✔✔A. 0.5987
✔✔You wish to test the claim that u> 132 at a level of significance of a = 0.05 and are
given sample statistics
n=40.7 = 137, and s= 14.2.
Compute the value of the test statistic and critical values.
Round your answer to two decimal places.
Let
t0.025 ; 39=2.023 - ✔✔B. 2.23 and 1.685
✔✔Suppose that the following is to be tested:
, Ho: p=0.72 and H₁: p ≠0.72.
Calculate the test statistic for the following sample data: Sixty-eight out of ninety test
subjects have the characteristic of interest
Round to the nearest thousandth. - ✔✔C. 0.751
✔✔A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24
students are randomly selected, find the probability at the mean of their test scores is
less than 70.
Let
P(Z < -1.88)= 0.0301, P(Z < 1.28) = 0.8997 - ✔✔E. 0.0301
✔✔If Z is a standardized normal variable, find the probability P(Z > 0.59).
Let P(Z < 0) = 0.5, P(Z < 0.59) = 0.7224, P(Z < 0.77) = 0.7810. - ✔✔E. 0.2776
✔✔Using the following uniform density curve, answer the question.
What is the probability that the random variable has a value greater than 5.3? - ✔✔B.
0.3375
✔✔A simple random sample of 5-year-old boys from a city is obtained and their weights
are listed below.
50 38 58 51 34 89 57 44 75 27 64
Use a 0.05 significance level to find the critical value to test the claim that the
population mean is smaller than 50. Assume that population has normal distribution.
Let
Z0.025= 1.96; t0.025,10-2.23
Z0.05= 1.65; t0.05,10=1.81 - ✔✔-1.81
✔✔The principal randomly selected six students to take an aptitude test. Their scores
were:
77.9 89.1 80.7 78.6 74.4 82.0
Determine a 90% confidence interval for the mean score for all students. Assume that
the population has a normal distribution.
Let t0.05,5 = 2.02 - ✔✔C. (76.35: 84.55)
ANSWERS TAGGED A+
✔✔Carter Motor Company claims that its new sedan, the Libra, will average better than
30 miles per gallon in the city. Use μ, the true average mileage of the Libra, express the
null hypothesis H0 and the alternative hypothesis H1 in symbolic form.
(i) H0: μ = 30; H1: μ < 30
(ii) H0: μ < 30; H1: μ ≥30
(iii) H0: μ = 30; H1: μ > 30
(iv) H0: μ > 30; H1: μ ≤30 - ✔✔C. (iii)
✔✔The scores of a final exam in Math are normally distributed with mean of 73 with
standard deviation 78. If 24 students are randomly selected, find the probability that the
mean of their test scores in greater than 78
Let P(Z <314)-0.9992. PIZ-1.26)-0.8962 - ✔✔B 0.0008
✔✔Use the margin of error.
confidence level, and standard deviation to find the minimum sample size required to
estimate an unknown population mean.
Margin of error: $126. confidence level: 99%, standard deviation = $534.
Let z0.005 = 2.58 - ✔✔B. 120
✔✔The volumes of soda in quart soda bottles are normally distributed with a mean of
32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of
soda in a randomly selected bottle will be less than 32 oz?
Let P(Z < 0.25) = 0.5987, P(Z < -0.3) = 0.3821. - ✔✔A. 0.5987
✔✔You wish to test the claim that u> 132 at a level of significance of a = 0.05 and are
given sample statistics
n=40.7 = 137, and s= 14.2.
Compute the value of the test statistic and critical values.
Round your answer to two decimal places.
Let
t0.025 ; 39=2.023 - ✔✔B. 2.23 and 1.685
✔✔Suppose that the following is to be tested:
, Ho: p=0.72 and H₁: p ≠0.72.
Calculate the test statistic for the following sample data: Sixty-eight out of ninety test
subjects have the characteristic of interest
Round to the nearest thousandth. - ✔✔C. 0.751
✔✔A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24
students are randomly selected, find the probability at the mean of their test scores is
less than 70.
Let
P(Z < -1.88)= 0.0301, P(Z < 1.28) = 0.8997 - ✔✔E. 0.0301
✔✔If Z is a standardized normal variable, find the probability P(Z > 0.59).
Let P(Z < 0) = 0.5, P(Z < 0.59) = 0.7224, P(Z < 0.77) = 0.7810. - ✔✔E. 0.2776
✔✔Using the following uniform density curve, answer the question.
What is the probability that the random variable has a value greater than 5.3? - ✔✔B.
0.3375
✔✔A simple random sample of 5-year-old boys from a city is obtained and their weights
are listed below.
50 38 58 51 34 89 57 44 75 27 64
Use a 0.05 significance level to find the critical value to test the claim that the
population mean is smaller than 50. Assume that population has normal distribution.
Let
Z0.025= 1.96; t0.025,10-2.23
Z0.05= 1.65; t0.05,10=1.81 - ✔✔-1.81
✔✔The principal randomly selected six students to take an aptitude test. Their scores
were:
77.9 89.1 80.7 78.6 74.4 82.0
Determine a 90% confidence interval for the mean score for all students. Assume that
the population has a normal distribution.
Let t0.05,5 = 2.02 - ✔✔C. (76.35: 84.55)
