In April 2025
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The records of SCA Registrar show that the average final grade in Mathematics for STEM
students is 91 with a standard deviation of 3. A group of student-researchers found out that
the average final grade of 37 randomly selected STEM students in Mathematics is no longer
91. Use 0.05 level of significance to test the hypothesis and a sample mean within the range
of 88 to 94 only.
A. State the hypotheses.
B. Determine the test statistic to use.
C. Determine the level of significance, critical value, and the decision rule.
D. Compute the value of the test statistic.
E. Make a decision.
F. Draw a conclusion.
234 members. Their mean is 3.5 and standard deviation 2.9
What is the 97.5th percentile in a t distribution with a sample size of 15
Determine whether the following given is a parameter or statistic.
1. The average weight of all males in the United States.
2. The average height of 100 cats in the state of California.
3. The average test of 20 students in a class of 500.
4. The average test score of all students in a class.
two incandescent lights are chosen at random from 19 lights of which 4 are defective. Find the probability that (a) none is defective? (b) exactly one is defective?
A lightbulb manufacturer regularly advertises that his bulbs last for at least 900 hours with
a standard deviation of 75 hours. A random sample is chosen before each campaign to
make sure that the claim is correct. If one such sample of 20 bulbs shows a mean of 925
hours, can the advertising claim be considered true at 0.05 level of significance?
Step Solution
1. State the null and alternative hypothesis
concerning the population mean, ΞΌ and the
type of test to be used
2. Specify the level of significance Ξ±
3. State the decision rule.
4. Collect the data and perform calculations.
5. Make a statistical decision.
6. State the conclusion.
Out of 1000 balls, 50 are red and the rest white. If 60 balls are picked at random, what is the probability of
picking up (1) 3 red balls (2) not more than 3 red balls in the sampl
Give the notation and area of these z score
1. above π§ = β2.4
2. below π§ = 0.2
3. Between π§ = β2.3 πππ
π§ = β0.98
4. at least π§ = 0.23
5. Between π§ =β1.23 πππ π§ =2
A. Areas under the Normal Curve: Find the area of the following. Then, illustrate using the
normal curve.
1. π§ = 0.34
2. π§ = 2.12
3. π§ = β1.35
4. π§ = β0.27
5. π§ = 1.07
6. At least π§ = β0.47
7. Between π§ = 0.76 πππ π§=2.34
8. Greater than π§ = 0.78
9. Less than π§ = β0.67
10. Between π§ =β1.52 πππ π§=0.97
Apply the Normal Curve concepts to solve each of the following. Show your complete solution
and illustration.
2. Most graduate schools of business require applicants for admission to take the Graduate
Management Admission Councilβs GMAT examination. Scores on the GMAT are roughly
normally distributed with a mean of 506 and a standard deviation of 96.
a. What is the probability of an individual scoring above 520? (with illustration)
b. What is the probability of an individual scoring below 506? (with illustration)
c. What is the probability of an individual scoring from 387 to 712? (with illustration)
3. Given π=45, and π=5.5.
a. What is the raw score when π§=β1.57?
b. What is the raw score when π§=2.09?
c. What is the raw score when β0.48<π§ <1.4?
d. What is the raw score when β2.17<π§ <1.79?
e. What is the raw score when π§=0.09?
