Question

1 part a) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 30 minutes. The owner has randomly selected 17 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 30 minutes. Suppose the P-value for the test was found to be 0.0266. State the correct conclusion.

A) At α = 0.05, we fail to reject H0.

B) At α = 0.03, we fail to reject H0.

C) At α = 0.02, we reject H0.

D) At α = 0.025, we fail to reject H0.

part b) According to insurance records a car with a certain protection system will be recovered 93% of the time. Find the probability that 5 of 9 stolen cars will be recovered.

A) 0.93

B) 0.002

C) 0.07

D) 0.556

part c) Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1 through 6, and 4 yellow disks numbered 7 through 10, find the probability of selecting a yellow disk, given that the number selected is less than or equal to 3 or greater than or equal to 8.

A) 3/5

B) 1/2

C) 3/4

D) 3/10

part d) The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 5.0 minutes and a standard deviation of 1 minute. Find the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot.

A) 5.5 min

B) 5.8 min

C) 5.7 min

D) 5.3 min

Answer 1

a)

if P-Value is less than level of significance (alpha) then we reject H0

here P-Value is 0.0266 which is less than alpha=0.05 Hence we reject H0 while for Alpha =0.025 we fail to reject as

P-Value > alpha so

D) At α = 0.025, we fail to reject H0.

b)

P(recovering the car) =p=0.93

let X is number of recovered cars out of stolen 9 cars

so X will follow Bin(9,0.93)

we have to find P(X=5)

c)

total number of disks =10

6 are green number from 1 to 6

4 yellow number from 7 to 10

we have to find P(yellow disk| number less than or equal to 3 or number greater than or equal to 8)

P(number less than or equal to 3 or number greater than or equal to 8) =P(getting number 1,2,3,8,9,10)

=6/10 =0.6

P(yellow disk and number less than or equal to 3 or number greater than or equal to 8) =P( getting number 8,9,10)

=3/10 =0.3

so required probability =0.3/0.6 =0.5

B) 1/2

d)

Let X is time then X is normal with mean =5 and SD=1

let cut off time is "a" so

P(X>a) =0.758

now

now from Z table P(Z<0.7) =0.758

so

so correct option is C) 5.7 min