Question

H al Random Variable n=30 2. It has been reported that 39% of college students graduate in 4 years. Consider a random sample of thirty students, and let the random variable X be the number who graduate in 4 years. a. Find the probability that exactly 13 students in the sample of 30 graduate in 4 years. b. Find the probability that 15 or fewer students in the sample graduate in 4 years. That is, find PIX S15). c. Using the results found in part b, calculate by hand the probability that more than 15 students in the sample graduate in 4 years.

Answer 1

Answer:

Given,

sample n = 30

p = 39% = 0.39

Mean = np = 30*0.39 = 11.7

standard deviation = sqrt(npq) = sqrt(30*0.39*0.61) = 2.6715

a)

Consider P(X) = nCr*p^r*q^(n-r)

P(X = 13) = 30C13*0.39^13*(1-0.39)^(30-13)

= 119759850*0.39^13*0.61^17

= 0.1296

b)

P(X <= 15) = P((x-u)/s < (15.5 - 11.7)/2.6715)

= P(z < 1.4224)

= 0.9225449 [since from z table]

= 0.9225

c)

P(X > 15) = 1 - P(X <= 15)

= 1 - 0.9225

= 0.0775