Question

1.- A random variable follows a binomial distribution with a probability of success equal to 0.72. For a sample size of n=12​, find the values below.

a. the probability of exactly 5 successes

b. the probability of 6 or more successes

c. the probability of exactly 11 successes

d. the expected value of the random variable

a. The probability of exactly 5 successes is

​(Round to three decimal places as​ needed.)

b. The probability of 6 or more successes is

​(Round to three decimal places as​ needed.)

c. The probability of exactly 11 successes is

​(Round to three decimal places as​ needed.)

d. The expected value of the random variable is

​(Type an integer or a decimal. Do not​ round.)

2.- A restaurant in a fast food franchise has determined that the chance a customer will order a soft drink is 0.87. The probability that a customer will order a hamburger is 0.58. The probability that a customer will order french fries is 0.45. Complete parts a and b below.

a. If a customer places an​ order, what is the probability that the order will include a soft drink and no fries if these two events are​ independent? The probability is

​(Round to four decimal places as​ needed.)

b. The restaurant has also determined that if a customer orders a​ hamburger, the probability the customer will order fries is 0.83. Determine the probability that the order will include a hamburger and fries.The probability is

​(Round to four decimal places as​ needed.)

Answer 1

1)

geven þ.0.71, M12 a) PC*5) (%) (044c1-6-72318-5 Plx-s) 0.021 b) PCX > 6) P (6)+ PC ) + P(B)+P19) +...+P(12) 1- P(x86) : 1- P(x?5) 1- [PColApli) + PC 2) + P(3)+P14) +PIS) : 1-[6380-78C1-0172)472 :1-[0+0+0 +0.001 +0.005+0.02)] ☺ 1 D.027 0.973 c) P (X=11) (43) (0.72)" (1-0.72) 72)"c1-0.7212-1 0.092 d) Mean Usmp- 1960-72) 8.64 Mean