Question

1-A contractor decided to build homes that will include the middle 80% of the market. If the average size of homes built is 1750 square feet, find the maximum and minimum sizes of the homes the contractor should build. Assume that the standard deviation is 96 square feet and the variable is normally distributed.

2-Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 13, p = 0.7, P(Fewer than 4)

3-A student takes a 5 question multiple choice quiz with 4 choices for each question. If the student guesses at random on each question, what is the probability that the student gets exactly 2 questions correct?

4- An investor is considering a $15,000 investment in a start-up company. She estimates that she has probability 0.15 of a $10,000 loss, probability 0.1 of a $10,000 profit, probability 0.3 of a $30,000 profit, and probability 0.45 of breaking even (a profit of $0). What is the expected value of the profit? $11,500 $15,250 $10,000 $8,500

Answer 1

1)

Answer

minimum sizes of the homes =1672.12

maximum sizes of the homes= 1872.88

2)

2-Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 13, p = 0.7, P(Fewer than 4)

Answer : 0.0007

3)

• let us consider p is the probability of correct guess = 1/4 = 0.25

  and q is the probability of incorrect guesses = 1-0.25 = 0.75

  number of question in quiz = 5

  since this is the case of Binomial distribution so

  P(exactly 2 correct) = 5C2[0.25]2[0.75]3 = 0.264

• P(exactly 2 correct) =0.264

4)

Answer

The expected value of the profit = $8500