Question

According to Harper's Index, 60% of all federal inmates are serving time for drug dealing. A random sample of 17 federal inmates is selected.

(a) What is the probability that 13 or more are serving time for drug dealing? (Use 3 decimal places.)


(b) What is the probability that 4 or fewer are serving time for drug dealing? (Use 3 decimal places.)


(c) What is the expected number of inmates serving time for drug dealing? (Use 1 decimal place.)

2.Given that x is a normal variable with mean μ = 42 and standard deviation σ = 6.5, find the following probabilities. (Round your answers to four decimal places.)

(a)  P(x ≤ 60)
(b)  P(x ≥ 50)
(c)  P(50 ≤ x ≤ 60)

3. Find z such that 19% of the area under the standard normal curve lies to the right of z. (Round your answer to two decimal places.)

4.Find z such that 68% of the standard normal curve lies between −z and z. (Round your answer to two decimal places.)

Answer 1

1

Binomial Distribution

n = 17

p = 0.6

q = 1 - p = 0.4

(a) P(X13):

So,

P(X13) = 0.126

(b)

P(X4):

So,

P(X4) = 0.0025

(c)

Expected number = np = 17 X 0.6 = 10.2

AS PER GUIDELINES FOR ANSWERING, FIRST FULL QUESTION IS ANSWERED.