Consider the rates of children (under 18 years of age) living in New York with grandparents as their primary caretakers. A sample of 13 New York counties yielded the following percentages of children under 18 living with grandparents. 9 4.0 5.7 5.1 4.1 4.4 6.5 4.4 5.8 5.1 6.1 4.5 4.9 a) Obtain and interpret the quartiles. b) Determine and interpret the interquartile range. c) Find and interpret the five-number summary.
Question Number 01
Consider the rates of children (under 18 years of age) living in New York with grandparents as
their primary caretakers. A sample of 13 New York counties yielded the following percentages of
children under 18 living with grandparents.
9 4.0 5.7 5.1 4.1 4.4 6.5 4.4 5.8 5.1 6.1 4.5 4.9
a) Obtain and interpret the
b) Determine and interpret the
c) Find and interpret the five-number summary.
Question Number 02
a) Given the cumulative distribution
?(?) =
{
0 ? < 1
0.25 1 ≤ ? < 3
0.5
0.75
1
3 ≤ ? < 5
5 ≤ ? < 7
? ≥ 7
Find
i) P(X=3)
ii) P(X>5)
iii) P(1.25<X<6.1)
b) Measurements of scientific systems are always subject to variation, some more than others.
There are many structures for measurement error, and statisticians spend a great deal of time
modelling these errors. Suppose the measurement error X of a certain physical quantity is
decided by the density function
?(?) = {
?(3 − ?
2
) −1 < ? < 1
0 ?????ℎ???
i) Determine k that renders f(x) a valid density function.
ii) Find the probability that a random error in measurement is more than 0.3.
Question Number 03
a) The density function of coded measurements of the pitch diameter of threads of a fitting is
?(?) = {
4
?(1 + ?
2)
0 < ? < 1
0 ?????ℎ???
Find the
B) A large industrial firm purchases several new word processors at the end of each year, the
exact number depending on the frequency of repairs in the previous year. Suppose that the
number of word processors, X, purchased each year has the following probability distribution:
X 1 2 3 4
f(x) 0.3 0.2 0.1 0.4
If the cost of the desired model is PKR 14500/= per unit and at the end of the year a refund of
32?
2
rupees will be issued, how much can this firm expect to spend on new word processors
during this year?
c) Consider the density function:
?(?) = {
6?(1 − ?) 0 < ? < 1
0 ?????ℎ???
i) Find ? and ?.
ii) Compute ?(? − ? < ? < ? + ?)
b) A new automated production process has an average of 1.5 breakdowns per day. Because of
the cost associated with a breakdown, management is concerned about the possibility of
having three or more breakdowns during a day. Assume that breakdowns occur randomly, that
the probability of a breakdown is the same for any two time intervals of equal length, and that
breakdowns in one period are independent of breakdowns in other periods. What is the
probability of having three or more breakdowns during a day?
Question Number 05
a) The amount of time required for routine automobile transmission service is
distributed
plans to have work begin on the transmission of a customer’s car 10 min after the car is
dropped off, and the customer is told that the car will be ready within 1 hr total time. What is
the probability that the service manager will be wrong? Illustrate the proportion of area under
the normal curve which is relevant in this case.
b) A contractor claims that the cost of building a farm house is a normally distributed random
variable with a mean of $500,000 and a standard deviation of $50,000.
i) What is the probability that the cost of building a home will be between $460,000 and
$540,000?
ii) The probability is 0.2 that the cost of building will be less than what amount?
Question Number 06
a) Assume that for the population of MBA (Supply Chain Management), the average starting
salary is PKR 72,000/= and the standard deviation of PKR 20,000/=. What is the probability
that a simple random sample of MBA (Supply Chain Management) will have a sample mean
within PKR 68,000/= and PKR 74,000/= when sample is (i) n=50 and (ii) n=100. Conclude
your result.
b) From 1200 accounts receivable, an auditor randomly draws simple random sample of size 40.
The population mean of the accounts receivable $362, with the population standard deviation
of $50. What is the probability that the sample mean will be less than $350.00?
Question Number 07
a) During a laboratory analysis of human blood composition, tests are repeated and are known
to be normally distributed. Fifteen tests on a given sample of blood yielded the following
values
1.003 1.01 1.03 1.045 1.006
1.024 1.019 1.009 1.014 1.021
1.031 1.08 1.058 1.012 1.001
Calculate the 98% confidence interval for true composition of the blood in repeated tests of
the sample.
b) Data on investments in the high-tech industry by venture capitalists are compiled by
VentureOne Corporation. A random sample of 16 venture capital investments in the fiber
optics business sector yielded the following data, in millions of dollars.
5.60 6.27 5.96 10.51 2.04 5.48 5.74 5.58
8.63 5.95 6.67 4.21 7.71 9.21 4.98 8.64
Determine a 99% confidence interval for the mean amount, μ, of all venture-capital
investments in the fiber optics business sector. Assume that the population standard
deviation is $1.98 millione
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