Statistics and Probability Answers

1.​The salaries of the employees in a company follow the normal distribution with mean $16000 and standard deviation $800.

(a)​What is the probability that the salary of an employee is higher than $18000?​​​​​​​​​​​​ (3 marks)
(b)​There is 80% chance that the salary of an employee is less than $t. Find the value of t.​​​​​​​​​​​
​​​​​​​​​​​​ (3 marks)
(c)​If 20 employees are randomly chosen from the company and the mean salary of the employees is calculated. The manager of the company claims that over 20% of the mean salaries of the employee are higher than $16200. Do you agree?

A rectangle with height and width equal to 3 and 25 respectively, is drawn on a checkered paper. Bazil paints a random horizontal 1×2 rectangle, and Peter paints a random vertical 2×1rectangle (each rectangle consists of 2 sells). Find the probability that at least one of the cells is painted twice. Express the answer in percent, and round to the nearest integer.

According to the All Pakistan Software Developer Association (APSDA), developers generally spend more than 40 hours each week working on software and web development. The Table 4.1 shows the number of hours worked per week for a sample of 15 Software developers and a sample of 10 Web developers.

Table 4.1
Software Developers 56 54 54 49 61 48 58 60 59 53 50 58 55 57 52
Web
Developers 47 50 46 47 48 49 46 55 44 42 ----


a) What is the third quartile of spending working hours for Software developers?
b) Create a box plot for the number of hours worked for Software developers.
c) Create a box plot for the number of hours worked for Web developers.
d) Comment on the differences between the box plots for Software & Web developers.

A rectangle with height and width equal to 3 and 25 respectively, is drawn on a checkered paper. Bazil paints a random horizontal 1×2 rectangle, and Peter paints a random vertical 2×1rectangle (each rectangle consists of 2 sells). Find the probability that at least one of the cells is painted twice. Express the answer in percent, and round to the nearest integer.

The first four deviations from the mean in a sample of reaction times were .3,
.9, 1.0, and 1.3. What is the fifth deviation from the mean? Give a sample for
which these are the five deviations from the mean.

The May 1, 2009 issue of The Montclarian reported the following home sale
amounts for a sample of homes in Alameda, CA that were sold the previous
month (1000s of $): 590 815 575 608 350 1285 408 540 555 679
a) Calculate and interpret the samplemean and median.
b) Suppose the 6th observation had been 985 rather than
1285. How would themean and median change?
c) Calculate a 20% trimmed mean by first trimming the two
smallest and two largest observations.
d) Calculate a 15% trimmed mean

A box contains 10 red and 12 white rose flowers. Four flowers are picked up at random one by one without replacement. What is the probability that;
a. The first 3 flowers are red?
b. three are 2 red and 2 white flowers
c. at least 2 are red.

The mean score of 2000 students appearing for an examination is 34.4 and the standard deviation is 16.6. How many candidates may be expected to obtain marks
i) between 30 and 60
ii) less than 32
iii)greater than 36
iv)between 36 and 39.

A population consists of 10, 10, 14, 14, 16, 18 and 20.

i. Calculate the sample means for all possible random samples of size 2, that can be drawn from this population, without replacement.
ii. Verify that
a. = µ
b. = σ2 / n (N-n/N-1)
iii. Also draw all possible samples of size 2 with replacement and verify the following properties:-
a. = µ
b. = σ2 / n

The average life of certain type of small motors is 10 years with standard deviation of 2 years. Suppose that the life of motors is normally distributed. Then what percentage of motors will
i) Between 8 and 12
ii) Between 6 and 8
iii)between 10 and 12
iv)between 8 and 10
v)between 12 and 14