Question

It is estimated that 55% of the freshmen entering a particular college will graduate from that college in four years.

Answer 1

Answer:

Step-by-step explanation:

Let x be a random variable representing the number of freshmen that will enter and graduate from the college. This is a binomial distribution since the outcomes are two ways. It is either they graduate or they don't graduate. The probability of success, p = 55/100 = 0.55

The probability of failure, q would be 1 - p = 1 - 0.55 = 0.45

a) We want to determine P(x = 3)

From the binomial distribution table,

P(x = 3) = 0.34

b) A majority would be all 3 and above graduating. From the binomial distribution table,

P(x ≥ 3) = 0.26

c) mean = np

mean = 80 × 0.55 = 44

Standard deviation = √npq

Standard deviation = √80 × 0.55 × 0.45 = 4.45