Question

15. Suppose that in USA, nine percent of undergraduate students carry credit card balances greater  than $7000. Suppose 10 undergraduate students are selected randomly to be interviewed about  credit card usage. a. Is the selection of 10 students a binomial experiment? Explain. b. What is the probability that two of the students will have a credit card balance greater than  $7000? c. What is the probability that none will have a credit card balance greater than $7000? d. What is the probability that at least three will have a credit card balance greater than $7000?

Answer 1

Pr(Undergraduate students carry credit card balances greater than $ 7000) = 0.09

Number of undergraduate students selected = 10

(a) Here this random variable is distributed binomially where n = 10 and p = 0.09.

(b) Here if x is the random variable about number of selected undergraduate students

Pr(x = 2; 10 ; 0.09) = ¹⁰C₂ (0.09)²(0.91)⁸ = 0.1714

(c) Pr(x = 0 ; 10 ; 0.09) =  ¹⁰C₀ (0.09)⁰(0.91)¹⁰ = 0.3894

(d) P(x=0 )=$0.09\times0.91^{10}=0.3894161181$

P(x=1)=$0.09^1\times 0.91^9=0.3851368201$

P(x=2)=$0.09^2\times0.91^8=0.1714070463$

0.3894161181 + 0.3851368201 + 0.1714070463 = 0.9459599845

1 - 0.9459599845 = 0.0540400155