Question

Source:The 16. Population of College Cities College often make up a substantial portion of the population of college cities and towns. State College, Pennsylvania ranks first with 71.1% of its population made lege students. What is the probability that ina random sample of 150 people from State College, more than 50 students of col- up are not college students? Source: www.infoplease.com Ot f roctau.

Answer 1

15. Proportion that are college student = 0.711

Proportion that are not college student, p = 1- 0.711 = 0.289

Sample size, n = 150

Mean, µ = n*p = 150 * 0.289 = 43.35

Standard deviation, σ = √(n*p*(1-p)) = √(150 * 0.289 * 0.711) = 5.5517

Probability that more than 50 are not college students, P(X > 50) =

= P((X - µ)/σ > (50 - 43.35)/5.5517)

= P(z > 1.1978)

= 1 - P(z < 1.1978)

Using excel function:

= 1 - NORM.S.DIST(1.1978, 1)

= 0.1155

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16. Sample mean using excel function AVERAGE(), x̅ = x̅ = 43.4516

σ = 31, n = 31

90% Confidence interval :

At α = 0.1 two tailed critical value, z_c = ABS(NORM.S.INV(0.1/2)) = 1.645

Lower Bound = x̅ - z_c*σ/√n = 43.4516 - 1.645 * 31/√31 = 34.293

Upper Bound = x̅ + z_c*σ/√n = 43.4516 + 1.645 * 31/√31 = 52.610