A. The result of the test administered to Grade 11 students shows that the mean score is 95 with a standard deviation of 25. Assume that the scores are normally distributed. If 10 ten scores are selected randomly, determine the -scores corresponding to the following sample means.

Sample Mean

1. 110

2. 100

3. 95

4. 85

5. 70

B. Solve the following problems. Show your complete solution to support your answers.

1. The average time it takes for students to take a certain examination is 46 minutes with a standard deviation of 8 minutes. If 40 students are randomly selected, what is the probability that the average time it takes for them to finish the examination is less than 43.5 minutes?

2. A cup of a certain brand of ice cream contains an average cholesterol of 750 mg with a standard deviation of 55 mg. If 35 cups of ice cream are selected randomly, what is the probability that the average amount of cholesterol is between 720 mg and 770 mg.

3. The charging time of a certain brand of smartphone follows a normal distribution with a mean of 120 minutes and a standard deviation of 37.5 minutes. What is the probability that a random sample of 10 smartphones will have an average charging time less than 95 minutes?

4. A study of life expectancy in a certain city shows that the mean age at death was 71 years with a standard deviation of 15 years. If a sample of 50 people from this city is selected, what is the probability that the mean life expectancy will be less than 65 years?

5. An electronic company that manufactures resistors claims that their product has a mean resistance of 120 ohms with a standard deviation of 13 ohms. Find the probability that a random sample of 40 resistors will have an average resistance greater than 114 ohms.