A class has 80 students. Test 2 had a class average of 78 and a variance of 49. Answer the following 7 questions. (Assume Normal distribution). Assume a 90-80-70-60 = A-B-C-D scale. 1. What is the probability of getting an A?

2. How many will get an A?

3. What is the probability of getting a B?

4. What is the probability of getting a C?

Question 2)

There are 90 people in the restaurant. The probability of someone ordering a drink with the food is 60%. Use Normal approximation of Binomial Distribution to answer the following 6 questions.

1. What is the mean of the Normal distribution?

2. What is the standard deviation of the normal distribution?

3. What is the probability that exactly 50 people will order a drink?

4. What the probability that more than 50 people will order a drink?

5. What is the probability that less than 50 people will order a drink?

6. What is the probability that between 52 or more and 56 or less people will order a drink?

5. How many people will fail the class?

6. If the bottom 5% will get an F, what will be the cut-off score?

7. If the top 15% get an A, what is the cutoff score for an A?

Question 3)Pioneer company has given an aptitude test to 71 potential job applicants. The test score had an average of 81 and a standard deviation of 8. Aptitude tests are known to follow a t-distribution. Pioneer rejects the bottom 5% of the applicants right away. The top 5% are hired immediately at managerial positions. Answer the next 6 questions.
a. What is the degrees of freedom for this distribution?
b. What is the t-score for someone who has scored 93?
c. What is the cutoff score for those who'll be hired as managers?
d. What will be the cutoff score fro those who'll get rejected right away?
e. If we want to define the middle of the class (80%) to be average, what will be the lower cut-off scores?
f. If we want to define the middle of the class (80%) to be average, what will be the upper cut-off scores?

Question 4)Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Tests revealed that the tire's mileage is normally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 5 percent of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce?

Question 5)

The weights of the tomatoes is normally distributed. If the middle 83% weigh between 2.71 ounces and 5.03 ounces, then what is the mean weight of the tomatos?

Question 6)

Nobel Dylan has determined that 25% of all its MP3-songs sales are credit sales. A random sample of 75 sales is selected.

	What is the probability that the sample proportion will be greater than 0.34?
2.	What is the probability that the sample proportion will be between 0.196 and 0.354?
3.	What is the probability that the sample proportion will be less than 0.25?
4.	What is the probability that the sample proportion will be less than 0.10?

Question 7)As the sample size becomes larger, the sampling distribution of the sample mean approaches a_____________

Question8) I two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85, and standard deviations 12 and 15, respectively, then probability that the mean of the 1st sample will be larger than the mean of the 2nd sample is

Question 9)

In a large university, 20% of the students are business majors. A random sample of 100 students is selected, and their majors are recorded.

1.	Compute the standard error of the proportion.
2.	What is the probability that the sample contains at least 12 business majors?
3.	What is the probability that the sample contains less than 15 business majors?
4.	What is the probability that the sample contains between 12 and 14 business majors?

Question 10)If the probability of success p = 60% and there are 30 trials, what is the standard deviation of the Normal distribution?