Statistics and Probability Answers

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)?

An American Society of Investors survey found 30% of individual investors have used a discount broker. In a random sample of nine individuals, what is the probability:

a. Exactly two of the sampled individuals have used a discount broker?

b. Exactly four of them have used a discount broker?

c. None of them has used a discount broker? 

The mean height of a random sample of 133 people is 155 cm and a standard deviation of 15 cm. The proportion of persons taller than 200 cm

If 5 pieces of certain ribbon selected at random have mean breaking strength

of 169.5 pounds with standard deviation 5.7, do they confirm to the

specification mean breaking strength of 180 pounds.

Use t଴.଴ଵ = 3.747 with 4 d.o.f.

One-tailed test, o? is known, a = 0.05, n= 34