Statistics and Probability Answers

The data below represent statistics and probability end of semester examination marks of 30
students randomly selected from the population of students who registered for probability and
statistics during 2018/2019 academic year.
16 51 36 45 23 48
37 19 28 28 25 36
76 22 27 18 28 42
38 47 44 29 37 42
27 33 35 46 28 27
Using sturge’s approximation rule with all your answers in one decimal place,
construct a frequency distribution table as follows
Class
Boundary
Tally Frequency Class
midpoint
CF FX FX^2
Calculate the coefficient of skewness for the data set and interpret our result.

Following data of performance scores is available of employees working with a company. You are required to perform the following: a. Make the frequency distribution, Calculate the frequency and the Cumulative frequency b. Calculate the mean, median, quartiles and Mode c. Calculate the variance and the standard deviation Table: Performance score of the employees: TABLE BELOW 52 33 70 95 57 61 47 60 57 64 54 94 38 61 89 48 50 39 94 63 59 31 88 46 68 88 93 48 82 82 72 73 74 70 92 76 98 91 80 68 32 33 31 75 54 48 62 53 36 64 63 66 92 98 91 42 36 54 71 86 84 55 33 43 91 34 64 67 89 78 47 62 97 92 53 56 68 55 36 67 93 42 51 77 36 93 51 66 44 66 63 33 68 79 92 76 83 53 86 76 35 40 43 46 55 41 36 39 42 96 42 77 60 53 38 51 95 56 93 63 48 69 49 33 95 37 83 64 83 62 96 34 85 32 40 85 39 59 77 62 35 34 39 92 54 89 36 45 83 34 86 90 39 61 88 86 55 33 77 40 69 54 30 38 79 77 44 59 95 34 38 91 80 90 58 40 88 45 95 71 80 43 89 53 61 40 31 61 58 53 88 94 91 63 60 94 98 53 53 45 50 34 75 74 90 98 87 66

During a manufacturing process, 15 units are randomly selected each day
from the production line to check the percent defective. From historical
information it is known that the probability of a defective unit is 0.05.
Any time 2 or more defectives are found in the sample of 15, the process
is stopped. This procedure is used to provide a signal in case the
probability of a defective has increased.
• What is the probability that on any given day the production process will
be stopped? (Assume 5% defective.)

Consider the 300 households surveyed in the DASCO Electronics example that actually
purchased a large screen Television. These respondents were asked to identity how the
purchased was transacted
Type of Purchase No. of Respondent
In store 183
Internet 87
Mail Order 30

Calculate the probability of picking a household that purchased the television via Internet or
by Mail order if the one respondent is randomly selected from a sample of 300 household.

The Head of the Mathematics Department is interested to know whether there is any variation in the way the two instructors in the deprtment grade mathematics quiz for the mid-term examination. They were given the same set of 30 exam papers selected randomaly with the same marking scheame. The first instructor's grades have a variance of 52.3. The second instructor's grades have a variance of 89.9. Test the claim that the first instructor's variance is smaller at the 10% level of significance.

In Islamabad city the mean number of power outages is 4 per month. Find the
probability that in a given month,
a. There are exactly 3 outages
b. There are more than 2 outages.

Super bikes arrive in a 12 lot showroom. Inspections are carried out on six out of every 12. For
one lot, it is known 2 out of 12 do not meet the safety standards prescribed. What is the
probability that at least 2 out of the 6 that were tested from that lot will not meet safety
standards?

Statistics department data show that 20% of Pakistani age 18 and over holds a certificate of
matriculation. If 10 Pakistani national age 18 and above are randomly selected, find the
probability that at least 3 will have certificates of matriculation.

On average per month, a particular laboratory uses 15 points to identify and match a fingerprint from a crime scene with a suspect in the database. Calculate the following probabilities:
a. The probability of a successful match in a given month with either 12 or 17 points of identification.

Find the probability that a person tossing 3 coins will get either all heads or all tails for the second time on the fifth toss?



Select one:
a. 0.1069
b. 0.105
c. 0.256