Question

2) From past experience, a restaurant owner has determined that 40% of those who visit her restaurant will spend at least $125. If 8 people will visit her restaurant tomorrow, find the probability that:

(a) 4 will spend at least $125

(b) at least 7 will spend less than $125

(c) less than 7 spend at least $125

5) An applicant for a job has to take an aptitude test. Suppose that the time it takes to finish the test is normally distributed with mean time 69 minutes and standard deviation 8 minutes. Determine how much time an applicant should be given so that 97 percent of them will be able to complete the test.

Answer 1

dear student please post the question one at a time.

2) a) probability that thhe person who visit her restaurant will spend at least $125 is : p = 0.4

Total number of people who visit her restraunt is : n= 8

a) The probability that 4 will spend at least $125 is binomial

b) probability that the person will spend less than $125:: p=1-0.4=0.6

the probability at least 7 will spend less than $125: $P(X\geq 7)=\sum_{x=7}^{8}_{x}^{8}\textrm{C}(0.60)^x(1-0.6)^{8-x}=0.1064$

c) the probability that less than 7 spend at least $125: $P(X<7)=\sum_{x=0}^{6}_{x}^{8}\textrm{C}(0.40)^x(1-0.4)^{8-x}=0.9915$