Statistics and Probability Answers

Question 1
Every month a clothing store conducts an inventory and calculates losses from theft. The store would like to reduce the losses and is considering two methods. The first is to hire a security guard, and the second is to install cameras. To help decide which method to choose, the manager hired a security guard for 6 months. During the next 6-month period, the store installed cameras. The monthly losses were recorded are listed here. The manager decided that because the cameras were cheaper than the guard, he would install the cameras unless there was enough evidence to infer that the guard was better. What should the manager do?

Security guard: 355 284 401 398 477 254
Cameras: 486 303 270 386 411 435

A Random variable has a mean 10 and variance 4. Find
P(|X-10|≥3) b) P(5<X<15) using Chebeshev theorem

. The sales in a two wheeler showroom is exponentially distributed with mean equal to 4. If two days are selected at random, what is the probability that
a) on both days the sales is over 5 units b) the sale is over 5 units on at least one of the
two days.

. The Probability that Ram will hit a target is 0.56 and the Probability that Shyam will hit the target is 0.45. The Probability that both will hit the target is 0.25. Find the Probability that
i) at least one will hit the target
ii) exactly one will hit the target
iii) not more than will hit the target

At a cafeteria the customers arrive at an average of 0.3 per minute. The probability
that a)exactly 2 customers arrive in a 10 minute span b)2 or more customers arrive in a 10
minute span c) one customer arrives in a 5 minute span and one customer arrives in the next
minute span is

Three employees E1 ,E2 ,E3 of a software company try for the post of Team Leader. Their chances of succeeding are 4:3:3. The Probability that a certain employee E4 will be given pink slip when E1 ,E2 ,E3 is made Team Leader are 0.3,0.2,0.1 respectively. What is the Probability that E4 will not be given pink slip.

Three employees E1 ,E2 ,E3 of a software company try for the post of Team Leader. Their chances of succeeding are 4:3:3. The Probability that a certain employee E4 will be given pink slip when E1 ,E2 ,E3 is made Team Leader are 0.3,0.2,0.1 respectively. What is the Probability that E4 will not be given pink slip.

A road construction company tests the strength of the roads by testing 10km stretches which are core drilled. Compression strength of 12.5MPa is acceptable specification with a standard deviation of 1.625MPa. A sample of 50 stretches were tested and the mean of the sample was 11.5MPa.
a. Set the acceptable criteria for the road strength plan. If a one tailed limit α = 0.05 is used.
b. Should the section of 50 sections tested be accepted?

In a clothing factory employing female and male employees, it was observed the the average number of absences for male workers over a year is 15 with a standard deviation of 7; for female workers, the average number of absences is 10 with a standard deviation of 6. In an industry –wide survey 100 male employees and 50 female employees were sampled. What is the probability that the male sample will have at most three days more days absences than the female sample?

The table below shows the distribution of scores in a Statistics test given to a class of 40 students. The teacher decided to pass the upper 40% of these students

Class Limits f

91-97 2
84-90 3
77-83 7
70-76 15
63-69 6
56-62 4
49-55 3


1. What is the passing score?
2. What is the percentile rank of the student hwhose score is 80?