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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 Council’s 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 𝜇=45, and 𝜎=5.5.
a. What is the raw score when 𝑧=−1.57?
b. What is the raw score when 𝑧=2.09?
c. What is the raw score when −0.48<𝑧 <1.4?
d. What is the raw score when −2.17<𝑧 <1.79?
e. What is the raw score when 𝑧=0.09?
DIRECTIONS: Solve for the z-computed value of the following. Write your answer to the
nearest hundredths. Show the complete solution.
1. x̅ = 9.2 μ = 10 σ =3 n = 68
2. x̅ = 28.3 μ = 26 σ = 4.5 n = 80
3. x̅ = 72.2 μ = 75 σ = 5.8 n = 118
4. x̅ = 49.6 μ = 52 σ = 7 n = 160
5. x̅ = 92 μ = 100 σ = 12 n = 130
Replacement times of TV sets are reported to follow a normal distribution having a mean
of 8.5 years with standard deviation of 1.2 years.
a. If 30 TV sets are selected at random, what is the probability that the mean
replacement time is less than 8 years?
b. If 20 TV sets are selected, what is the probability that the mean replacement
time is longer than 7.8 years?
c. If 25 TV sets are randomly selected, what is the probability that the
replacement time is between 8.4 years and 9 years?
The mean NAT scores of Grade 10 students is 65. Sixty (60) students were chosen and
found that the standard deviation of their scores is 5. What is the probability that their
mean is between 64 and 67?
The mean NAT scores of Grade 10 students is 65. Sixty (60) students were chosen and
found that the standard deviation of their scores is 5. What is the probability that their
mean is between 64 and 67?
Consider A = <0,4,2> , B = <6,-1,0> , and C = <3,0,1>. Find scalars a, b and c such that aA + bB = (c - 1)C.
.
The Smith Trucking Company claims that the average weight of its delivery trucks when fully loaded is 6000 pounds with a standard deviation of 120 pounds. 36 trucks are selected at random and their weights recorded. Within what limits will the average weights of 90% of the 36 trucks lie?
A box contains 6 defective bulbs and 10 functional bulbs. If 4 bulbs are to be chosen at random. what is the probability that there are 2 defective bulbs and 2 functional bulbs selected?
A study reports that 5% of adults are afraid to be home alone at night. If 20 people are randomly selected, what is the probability at least 3 of them are afraid to be home alone at night?
A Random sample of 60 grade 11 students ages is obtained to estimate the mean ages of all grade 11 students. Suppose the sample mean is 17.3 and the population variance is 18,
1. What is the point of estimate of the population parameter?
2.Find the 95% confidence interval for the population parameter?
3.Find the 99% confidence interval for the population parameter?
