Statistics and Probability Answers

The masses of articles produced in a particular workshop are normally distributed with mean A and standard deviation B. 5% of the article have a mass greater than 85g and 10% have a mas less than 25g. Find the values of A and B.

two instruments have been designed to measure water pressure in a pipeline. One is known to be more accurate than the other but both are subjected to random error . The reading by instrument I and ll are subject to the standard deviations, q and 1.25q respectively . instrument l is used to take 6 independent measurements giving a mean of x , while instrument ll took 10 independent measurements with mean of x2 , suppose the two sample measurement are drawn from a product with mean o and variance o2, show that the estimators x and x2 are unbiased

A students is going to graduate from a business department of a university by the end of the
semester. After being interviewed at two companies he likes, he assesses that his probability of
getting an offer from company A is 0.6, and his probability of getting an offer from company B is
0.45. If he believes that the probability that he will get offers from both companies is 0.35, what
is the probability that he will get at least one offer from these two companies?

If the license plates in a Karachi consist of three letters followed by three numbers, what is the
probability that a randomly generated plate ends in the numbers “786”? Consider that repetitions
are allowed and order matters.

An University wishes to hire 4 faculty members for its newly established department. They have
to select from a group of 8 Male and 7 Female applicants, all of whom are equally qualified to
fill in the positions. If University selects 4 at random, what is the probability that ;
a) All four will be Men
b) All four will be Women
c) Atleast one will be a Women
d) Atleast one will be a Men

If the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and
the sum of the ages of all 3 is 147 years, what is the age difference between oldest the
youngest?

A sample of 150 people from a certain industrial community showed that 80 people suffered from a lung disease. A sample of 100 people from a rural community showed that 30 suffered from the same lung disease. At α=0.05, is there a difference between the proportions of people who suffer from the disease in the two communities? Use any method.

A liquid dietary product implies in its advertising that use of the product for one month results in an average weight loss of at least 3 pounds. Eight subjects use the product for one month, and the resulting weight loss data are reported below. Use hypothesis-testing procedures to answer the following questions. Initial Final Subject Weight (lb) Weight (lb) 1 165 161 2 201 195 3 195 192 4 198 193 5 155 150 6 143 141 7 150 146 8 187 183 (a) Do the data support the claim of the producer of the dietary product with the probability of a type I error set to 0.05? (b) Do the data support the claim of the producer of the dietary product with the probability of a type I error set to 0.01? (c) In an effort to improve sales, the producer is considering changing its claim from at least 3 pounds to at least 5 pounds. Repeat parts (a) and (b) to test this new claim.

A computer manager needs to know how efficiency of her new computer program depends
on the size of incoming data. Efficiency will be measured by the number of processed
requests per hour. Applying the program to data sets of different sizes, she obtains the
following results,
Data size (gigabytes) 6 7 7 8 10 10 15
Processed requests 40 55 50 41 17 26 16
i. Draw the scatterplot for the data. Be sure to label your axes.
ii. Is there any correlation between the processing request and the size of incoming data?
What is the correlation coefficient?
iii. By what percentage is the processing time dependent on the size of incoming data?

iv. Compute a least square regression line for regressing processing request on the size of
incoming data.
v. Use your regression equation to predict the processing request for an incoming data
of size 17.0 gigabytes
vi. Is the slope statistically significant at α = 5% ?

A student asks her teacher “What is the probability that it will take you exactly 20 minutes to walk to school in the morning?” What will be the teacher's reply? What is a better question to ask? Explain by referring to concepts that we discussed in this unit.