Question

A youth and money survey, sponsored by the american savings education council talked to 1,000 students about their personal finance, ages 16-22. The survey found that 33% of students in this age group have their own credit card. if a sub sample of 100 students is taken from this survey what is the probability that 40 or less will have their own credit card?

A.) Using the normal approximation for the binomial solve this problem, show all of your work in solving the problem.

Answer 1

Solution:

Given that,

P = 0.33

1 - P = 0.67

n = 100

Here, BIN ( n , P ) that is , BIN (100 , 0.33)

then,

n*p = 100 * 0.33 = 33 > 5

n(1- P) = 100 * 0.67 = 67 > 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 33

Standard deviation = =n*p*(1-p) = 100 * 0.33 * 0.67 = 22.11

We using continuity correction factor

P( X a ) = P(X < a + 0.5)

P(x < 40.5) = P((x - ) / < (40.5 - 33) / 22.11)

= P(z < 1.60)

Probability = 0.9452