Question

Probability and Statistics
Could you please solve the following questions with specifying the answers

A. If a baseball batter gets a hit 31% of the time, what is the probability his first hit occurs on his fourth time at bat?  

1. 22.7%       b. 10.2%     c.  14.7%    d.  7.1%

B. A dog can pass through one of three doors, A, B and C. If the dog is six times as likely to go through A as B, and it is three times as likely to go through C as B, what is the probability it will go through door B? (Hint: Let x =probability of going through B.)

a. 1/10        b. 1/8      c. 2/9      d. 1/9

C. A soda dispensing machine delivers volumes of soda normally distributed with mean 7.8 ounces and standard deviation .1 ounce. How often does the machine cause the 8 ounce cups to overflow?

a. 13.5%       b. 34%        c. 16%       d. 2.5%

Answer 1

A)

Using Geometric distribution

p = 0.31 , X : the 1st success on kth trail

P(x=4) = 0.31*(1-0.31)4-1 = 0.102 that is 10.2%

b. 10.2%

B.

From given information,

A= 6B

C = 3B

We know that A+B+C = 6B+B+3B = 10B implies B = 1/10

a. 1/10

C.

µ = 7.8
σ = 0.1

P(the 8 ounce cups to overflow) = P ( x > 8) = P((x-µ)/σ < (8-7.8)/0.1) = P(z>2.00)

Using empirical rule,

d. 2.5%