Question

Random samples of size n = 60 were selected from a binomial population with p = 0.2. Use the normal distribution to approximate the following probabilities. (Round your answers to four decimal places.)

(a)    

P(p̂ ≤ 0.22) =

(b)    

P(0.18 ≤ p̂ ≤ 0.22) =

Answer 1

n = 60, p = 0.2

is normally distributed with mean of = p = 0.2

& standard deviation, = == 0.05164

Z =

a) P(0.22) = P()

= P(Z0.39)

= 0.6517 (from z-table)

b) P(0.18 ≤ p̂ ≤ 0.22) = P(Z)

= P(-0.39Z0.39)

= P(Z0.39)-P(Z-0.39)

= 0.65173-0.34827

=0.30346

=0.3035