Question

In a survey conducted by a company, 40% of all cell phones calls are dropped in Seattle. Suppose that a random sample of 8 people are selected in Seattle. What is the probability that… (3 Decimal Places use round off rule) Exactly 8 calls are dropped? None are dropped? At least 6 calls are dropped? 1 or more calls are dropped? If 1200 people are randomly selected, what is the mean and standard deviation of dropped calls?

Answer 1

X ~ Bin ( n , p)

Where n = 8 , p = 0.40

binomial probability distribution is

P(X) = nCx * px * ( 1 - p)n-x  

a)

P(X = 8) = 8C8 * 0.48 * ( 1 - 0.4)0

= 0.001

b)

P(X = 0) = 8C0 * 0.40 * ( 1 - 0.4)8

= 0.017

c)

P(X >= 6) = P(X = 6) + P(X = 7) + P(X = 8)

= 8C6 * 0.46 * ( 1 - 0.4)2 +8C7 * 0.47 * ( 1 - 0.4)1 +8C8 * 0.48 * ( 1 - 0.4)0

= 0.050

d)

P(X >= 1) = 1 - P(X = 0)

= 1 - 0.017 (Probability calculated in part b)

= 0.983

e)

Mean = n p = 1200 * 0.40 = 480

Standard deviation = sqrt [ n p ( 1- p) ] = sqrt [ 1200 * 0.40 ( 1 - 0.40) ] = 16.9706