Statistics and Probability Answers

A continuous random variable has a density function f(x)= 2(5-x)/5 , where 2<x<3. Calculate
the following probability correct up to 3 decimal places, and make the graph for part (a) only in Answer sheet:
P (x < 2.5)
P (x > 2.2)
P (2.1 ≤

Mr.Escalona administired a 50 item to 345 students.The mean and standard deviation if the test is 35 and 5 respectively.Assuming it is normally distributed,find the approxiamate number of students who scored the ff.
a.more than 40
b.less than 30
c.between 32 and 38
d.exactly 45

A continuous random variable has a density function , where 2<x<3. Calculate
the following probability correct up to 3 decimal places, and make the graph for part (a) only in Answer sheet:
P (x < 2.5)
P (x > 2.2)
P (2.1 ≤

On the basis of the previous record, an average of 4 accidents in one day occur on the superhighway during peak rush timings. Calculate the following if possible. If any part of question (you feel) is not possible to calculate give reason:
a. Evaluate the probability that on any Particular day there will be fewer than 3 accidents on this superhighway during the peak rush timings.
b. Compute the probability that on any Particular day there will be more than 6 accidents on this Super highway during the peak rush timings.
c. Find the Expected number of accidents per day and variance.

The management of ‘Fun Land’ studied the waiting times for Dogging Car by children in waiting area before sit and drive a car. The following data with waiting times in minutes were collected over a one-month period. Consider the following data in Table 2.1:

Table 2.1
28 17 30 25 22
33 38 23 26 10
14 15 24 22 34
12 33 32 31 26
26 32 35 17 12
34 32 22 19 14
15 27 15 25 31
36 28 35 28 22
26 10 29 19 15
9 20 34 27 20

a) Develop a frequency distribution using classes of 9–14, 15–20, 21–26, 27–32, and 33–38. [1]
b) Develop a relative frequency distribution and a percent frequency distribution. [2]
c) Cumulative frequency and a cumulative relative frequency. [2]

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

The management of ‘Fun Land’ studied the waiting times for Dogging Car by children in waiting area before sit and drive a car. The following data with waiting times in minutes were collected over a one-month period. Consider the following data in Table 2.1:

Table 2.1
28 17 30 25 22
33 38 23 26 10
14 15 24 22 34
12 33 32 31 26
26 32 35 17 12
34 32 22 19 14
15 27 15 25 31
36 28 35 28 22
26 10 29 19 15
9 20 34 27 20

a) Develop a frequency distribution using classes of 9–14, 15–20, 21–26, 27–32, and 33–38.
b) Develop a relative frequency distribution and a percent frequency distribution.
c) Cumulative frequency and a cumulative relative frequency.

On the basis of the previous record, an average of 4 accidents in one day occur on the superhighway during peak rush timings. Calculate the following if possible. If any part of question (you feel) is not possible to calculate give reason:
a. Evaluate the probability that on any Particular day there will be fewer than 3 accidents on this superhighway during the peak rush timings.
b. Compute the probability that on any Particular day there will be more than 6 accidents on this Super highway during the peak rush timings.
c. Find the Expected number of accidents per day and variance.