Question

The manager of a gasoline supply corporation wants to estimate the actual amount of gasoline contained in standard 42-gallon barrels purchased from a nationally known manufacturer. The manufacturer’s specifications state that the amount of gasoline is normally distributed with a standard deviation of 0.65 gallon. A random sample of 25 barrels is selected, and the sample mean amount of gasoline per 42-gallon barrel is 42.15 gallons. Construct a 90% confidence interval estimate for the population mean amount of gasoline contained in a standard 42-gallon barrel.

Select one:

a. 42 ± 1.645 (0.65) / 5

b. 42.15 ± 1.7109 (0.65) / 25

c. 42 ± 1.7109 (0.65) / 25

d. 42.15 ± 1.645 (0.65) / 5

According to the regulation of a certain university, an undergraduate student may take a course more than once and only the course grade of the last attempt will appear on the student’s transcript. Assuming that a student took the course “University Mathematics” several times and the probability of him passing the course each time is 0.45. What is the probability that he passed the course at least two times out of five attempts?

Select one:

a. 0.7941

b. 0.3369

c. 0.7438

d. 0.6631

Answer 1

1)

Since , the population standard deviation is known.

Therefore , use normal distribution .

Now , ; From Z-table

Therefore , the 90% confidence interval estimate for the population mean amount of gasoline contained in a standard 42-gallon barrel is ,

Correct option : (d)

2)

Let ,

The PMF of X is ,

; x=0,1,2,........,n and q=1-p

=0 ; otherwise

The probability distribution table is given by ,

0	1	1	0.050328	0.050328
1	5	0.45	0.091506	0.205889
2	10	0.2025	0.166375	0.336909
3	10	0.091125	0.3025	0.275653
4	5	0.041006	0.55	0.112767
5	1	0.018453	1	0.018453

Now ,

Therefore , the probability that he passed the course at least two times out of five attempts is 0.7438

Correct option : (c)