Consider a binomial experiment with n=15 and .p=0.4 a. Compute f (0)  (to 4 decimals).   b. Compute f (13) (to 4 decimals).   c. Compute p (x less than equal to 4 )  (to 4 decimals).   d. Compute   p (x greater than equal to 2 )(to 4 decimals).     e. Compute E(x)  (to 1 decimal).   f. Compute  var (x) and .sd   (to 2 decimals)   (to 2 decimals)

Consider a binomial experiment with n = 14 and p = 0.3. a. Compute f(0) (to 4 decimals). f(0) = b. Compute f(5) (to 4 decimals). f(5) = c. Compute P(x 2) (to 4 decimals). P(x > 2) = e. Compute E(x) (to 1 decimal). E(x) = f. Compute Var(x) and o. Var(x) = (to 2 decimals) O = (to 2 decimals)

*11. Show that for the two-tailed test, the p-value is: Vn(Y – 60) 2 1- ¢

8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable X that follows an exponential distribution with mean 15 minutes. a) Find P(14 < X < 22). Round off your answer to two decimal places. x 22 1 P(14 < X <22) = √₂/1² 15 e 15dx = P(x < 22) — P(x < 14) x 15 122 = e 15 22 1 - e 14 or 0.8 = = 22 14 = −e 15 + e15 = 0.16254≈ 0.16 - (1 – b) Find the 80th percentile. Round off to the nearest whole number. 1 X S 15 14 e 15 t e 15 dt X 0.8 = 1 e 15 X e 15 = = 0.2 14 22 = e 15 e 15 = 0.16 x — = ln (0.2). This gives x = 24.14156 15

Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?

2. Find E(X) and Var(X) if a. P(X = 0) = 0.2, P(X = 1) = 0.3, and P(X = 2) = 0.5. b. X is the number of successes in 200 Bernoulli trials each with probability of success 0.7.