Question

The probability that a student likes statistics is .1.   What is the probability that 5 or less students like stats in a class of 16?

B. A firm wants to set its warranty so only 2% of its phones fail and must be replaced. The mean life of the phone is 800 days and the standard deviation is 25 days. How many days should the warranty be set?

C. the probability that Obama says “I” more than twice per minute in a news conference is 2/3. What is the probability he has 2 per minute ‘I’s conferences in 3 of 4 conferences?

Answer 1

A) n = 16

P = 0.1

It is a binomial distribution.

P(X = x) = nCx * p^xx * (1 - p) ^{n - x}x

P(X < 5)

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

= 16C0 * (0.1) ^0 * (0.9) ^16 + 16C1 * (0.1) ^1 * (0.9) ^15 + 16C2 * (0.1) ^2 * (0.9) ^14 + 16C3 * (0.1) ^3 * (0.9) ^13 + 16C4 * (0.1) ^4 * (0.9) ^12 + 16C5 * (0.1) ^5 * (0.9) ^11

= 0.9967

B) P(X < x) = 0.02

Or, P((X - ) / < (x - )/) = 0.02

Or, P(Z < (x - 800) /25) = 0.02

Or, (x - 800) /25 = -2. 05

Or, x = -2.05 * 25 + 800

Or, x = 748.75

C) P = 2/3

n = 4

P(X = 3) = 4C3 * (2/3) ^3 * (1/3) ^1 = 0.3951