Statistics and Probability Answers

QUESTION 1
The cumulative grade-point average (CGPA) for the top 25 undergraduates in one particular university are listed in Table 3,
Table 3
3.80 3.77 3.70 3.74 3.70
3.86 3.76 3.68 3.67 3.57
3.83 3.70 3.80 3.74 3.67
3.78 3.74 3.73 3.65 3.66
3.75 3.64 3.78 3.73 3.64

a) Calculate the mean, the median and the mode of the CGPA. (8 Marks)
b) Comment on the shape of the distribution of the CGPA based on the values gathered in (a). (2 Marks)

If x is a normal variable with the mean u=5 and variance (sigma square)=16, what is the probability that x is less than or equal to 6?

Let X has the discrete uniform distribution
f
(
x
)
=
1
k
f(x)=1k
for x=0,1,2…. , find the expression for its mean u

the web site for xyz gets approximately seven visitors per mintue.suppose the number of web site visitors per minutes per minute follows a poisson probability distribution
(1)what is the mean time between visits to the web site?
(2)what is the probability no one will access the web site in a 1 minute period?
(3)what is the probability no one will access the web site in a 12 second period?

When you toss 5 coins once, if the number of head(s) is the random variable define on the resulting sample space. What is the set of random variable resulting from this experiment?

A new drug is being tested to see whether it can
increase the chance of a full recovery in people
who have had arthroscopic knee surgery. The rate of full recovery in the population of concern is
0.82. Write the correct hypotheses

Which of the following statements about the sampling distribution of the sample mean X is not correct?

(a) For an infinite population, the standard error of the mean is always equal to the population standard deviation divided by the square root of the sample size.

or

(b) For a finite population of size N, the standard error of the mean is always equal to 1 N n n N Ï

Assume that on an average one telephone number out of 15 is busy. Which probability distribution can be used to find the probability that if 6 randomly selected telephone numbers are called, not more than three will be busy? Find the probability.

A sample of 25 items is selected from a very large shipment. It is found to have a mean weight of 310 gm and standard deviation equal to 9 gm. State and compute the 95% confidence limits for the population mean weight. (4) b) In a University, 20% of all students are graduates and 80% are undergraduates. The probability that a graduate student is married is 0.5 and the probability that an undergraduate student is married is 0.1. One student is selected at random. What is the probability that (i) he/she is married (ii) the student is a graduate if he/she is found to be married?

QUESTION 2
The amount of protein (in grams) for a variety of burgers from selected fast-food restaurants in Klang Valley is reported in Table 2.

Table 2
23 30 20 27 44 26 35 20 29 29
25 15 18 27 19 22 12 26 34 15
27 35 26 43 35 14 24 12 23 31
40 35 38 57 22 42 24 21 27 33

a) Construct a frequency distribution table using eight as the class width and 12 as (4)
the lower limit of the first class.
b) Based on the frequency table in (a), construct a histogram. (4)
c) Comment on the distribution of the protein based on the histogramconstructed (2)
in (b).