Statistics and Probability Answers

A random sample of the ACT scores of 400 students at Big State University provided a sample mean score of 22.48 with a sample standard deviation of 5.76. Find the p-value when testing the claim that u, the population mean ACT score, is greater than 22.
.024
.048
.096
.192
.256

which of the following confidence levels leads to the smallest margin of error?
90%
95%
97%
98%
99%

Assume that 90% of all industries contain shipping open order files in their computerized database. In a random sample of 10 industries, let X be the number that includes shipping open order files in their computerized database.
i) Find P(X=8)
ii) Find P(X>5)
iii) Find the mean and variance of X.

A random sample of 30 companies dealing in network products was selected to determine the proportion of such companies that have implemented new software to improve productivity. It turned out that 8 had implemented such software. Find a 95% confidence interval on p, the true proportion of such companies that have implemented new software and how many companies would need to be sampled in order to have a 95% confident that the estimate of p is within 0.05 of the true value?

A manager claimed that his employees perform better at work with music playing. An experiment was conducted to verify the manager's claim. One day, the music was turned on during working hours with 45 employees. It is found that the mean productivity level is 5.2 with standard deviation of 2.4. On a different day, the music was turned off and there were 40 employees with a mean productivity level of 4.8 and a standard deviation 1.2. Does the experiment support the manager's claim? Use 5% level of significance to solve.

There are two groups of subjects, one of which consists of 5 science subjects and 3 engineering subjects and the other consists of 3 science subjects and 5 engineering subjects. An unbiased die is cast. If number 3 or number 5 turns up, a subject is selected at random from the first group. Otherwise, a subject is selected random from the second group. Find the probability that an engineering subject is selected ultimately.

There are two winning tickets among ten tickets available. Determine the probability that (i) one or both of these tickets will be winning among five tickets selected at random.

A bag contains 9 white and one black ball. Three of them are taken out at a time from the bag. Find the probability that all balls taken out are white.

The card is taken out from a pack of 52 cards. The selection of each cards is equiprobable. In which of the following cases the events A and B are independent.
i. A: “The card drawn is a diamond”
B: “The card drawn is a knave”
ii. A: “The card drawn is a red”
B: “The card drawn is a queen”
iii. A: “The card drawn is a queen or king”
B: “The card drawn is a king or knave”

A bag contains 3 red and 4 black balls and another bag has 4 red, 2 black and 3 green balls. The selection of the two bags are equiprobable. A bag is selected at random. From the selected bag a ball is taken out. The drawing of each ball is also equiprobable.
A is the event: “the first bag is selected”
B is the event: “the second bag is selected”
H is the event: “the ball drawn is red”
Then find P(A), P(B), P(H/A) and P(H/B).