Question

A local county has an unemployment rate of 8%. A random sample of 15 employable people are picked at random from the county and are asked if they are employed. The distribution is a binomial. Round answers to 4 decimal places. a) Find the probability that exactly 5 in the sample are unemployed. b) Find the probability that there are fewer than 2 in the sample are unemployed. c) Find the probability that there are more than 1 in the sample are unemployed. d) Find the probability that there are at most 2 in the sample are unemployed.

Answer 1

Given: Unemployment rate p= 0.08 Sample size n = 15 Of x is the number of people un employed out of 15; x Binomial (n=15, P-0-08) :- P(x.x'). "C_0.08)*(0-0.08) - * Ta 15-5 @ poobability that exactly 5 in the sample age unemployed = P(x - 5) 15€(0.08)*(1-0-08) 15€ (0.08)" (0.92) 10 2 3003* 0-0000032768* 0.434388 0.0043 5 P (fewer than a in the sample as unemployed) =P (x2a) - P(x=0)4p(221) 15€ 6.05)°C-9237156, 66.08)"@-92)14 2 I* 1 * 0.2863 + 15 * 0-08*0.31119 0.2863+ 0.373428 ♡0- 6597 © P (more than I in the sample are unemployed)= P(x >1)=1-{px=1 1-[P&=0) + P(x=1] 1 - [0.2863+0. 286370-373428 [p@=o), pkzi) au calculated in 1 -0.6597 = 0.3403 2 P[at most a in the sample are unemployed] - P[x<2] P[x>0}+p[x + p [x>]]+P[x>2). P[1,2] =', 6.08)*0.9219 6.08)*0.92)3-105* 0.0064 * 0-33825 z 0 - 2273 .: p(x32) = 0.2863 +0-3734 +0.2273 - 0.8870