In April 2025
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I. Apply the Normal Curve concepts to solve each of the following. Show your complete solution
and illustration.
Suppose the current annual salary of all teachers in the Philippines have a normal distribution with a mean of 95,000 pesos and a standard deviation of 20,000 pesos.
a. Find the probability that the annual salary of a randomly selected teacher would be between 56,000 and 76,000.(with illustration)
b.Find the probability that the annual salary of a randomly selected teacher would be at least 50,000 pesos. (with illustration)
c. Find the probability that the annual salary of a randomly selected teacher would be 126,000 pesos. (with illustration)
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?
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 student 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 estimate of the population parameter?
2. Find the 95% confidence interval for the population parameter?
3. Find the 99% condence interval for the population parameter?
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?
