Question

According to a marketing research firm, 31% of people do not own a credit card. If a random sample of 208 people are chosen, what is the probability that between 25% and 33% do not own a credit card? (Give your answer with 4 decimals

Answer 1

Solution

Given that,

p = 0.31

1 - p = 1-0.31=0.69

n = 208

= p =0.31

=  [p ( 1 - p ) / n] = [(0.31*0.69) / 208 ] = 0.03207

= P( 0.25 << 0.33)= P[(0.25-0.31) / 0.03207< ( - ) / < (0.33-0.31) /0.03207 ]

= P(-1.87 < z <0.62 )

= P(z <0.62) - P(z < -1.87)

Using z table

=0.7324-0.0307

=0.7017

probability= 0.7017