Statistics and Probability Answers

A hog raiser in a certain province uses two methods of pig-farming: intensive pig farming, where pigs are housed indoors in group-housing or straw-lined sheds; and extensive pig farming, where pigs are allowed to wander around the farm or fence. Test the hypothesis whether or not the mean weight of pigs in intensive farming is better than the extensive farming based from the mean weight of the pigs in the sample with data shown below. Use a one-tailed test at 𝛼 = 1%. Determine the Zcritical value of the problem above.

Solve for the t-computed value of the following. Write your answer to the nearest

hundredths. Show the complete solution.

1. "\\chi" =15 "\\mu" = 12 s = 4 n = 12
2. "\\chi" = 7.8 "\\mu" = 10 s = 5.1 n = 10
3. "\\chi" = 5 "\\mu" = 5.3 s = 0.14 n = 8
4. "\\chi" = 7.2 "\\mu" = 9.1 s = 1.8 n = 15
5. "\\chi" = 5 "\\mu" = 7 s = 3 n = 10

Given 𝜇 = 45, and 𝜎 = 5.5. (7 points)

a. What is the raw score when 𝑧 = −1.57?

b. What is the raw score when 𝑧 = 2.09?

c. What is the raw score when −0.48 < 𝑧 < 1.4?

d. What is the raw score when −2.17 < 𝑧 < 1.79? e. What is the raw score when 𝑧 = 0.09?

Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 506 and a standard deviation of 96. (14 pts)

a. What is the probability of an individual scoring above 520? (with illustration, 6 pts)

b. What is the probability of an individual scoring below 506? (with illustration, 4 pts)

c. What is the probability of an individual scoring from 387 to 712? (with illustration, 4 pts)

If a freshman is selected at random to become student assistant, what is the probability of selecting a student with an IQ between 90 and 120? Draw the normal curve.

A deck (52) of cards (clubs, diamonds, hearts and spades) is shuffled once. Estimate the probability of drawing a king and queen. Estimate the probability of drawing a 4 (four). Estimate the probability of drawing a card that is not a heart.

A random variable x is normally with mean 10 and variance 6.25 what is the value of p(x>12.25)

A gambler plays only one game for at most one hour each evening. The chance of showing a profit at the end of the hour if he plays roulette and blackjack is 30% and 20% respectively. He chooses blackjack on 60% of the evenings and roulette on the remaining evenings. Suppose he shows a profit after playing one a particular evening. What is the probability that that he played blackjack?

A prisoner is considering his chances of escape. From his cell, there are 3 possible exits he could choose and if he chooses a particular exit, the probability he will escape is 0.4; 0.3 and 0.4 respectively. If the prisoner picks an exit at random, what is the probability that the prisoner will make a successful escape (to 3 decimal places)?