(STAT-101) Assignment NO. 2 complete solutions correct answers key

(STAT-101) Assignment NO. 2 complete solutions correct answers key

STATISTICS


Total Points
True/False

____/5

MCQ

____/5

Short Answer

____/15

Total

____/25

Good Luck

STATISTICS (STAT-101)

Marks- 25
Answer all the Questions on the same question paper.

Section-I
State whether the following statements are True or False. (5 marks, 1 Mark
Each)
1. Mean value over an infinite number of observations of the variables is the
expected value of random variables.
2. A standard normal distribution has the mean equal to the variance.
3. A sampling distribution of the mean ̅ has mean of µ and standard

deviation of .
√
4. A critical value is a z score separating unlikely values from those that are
likely to occur.
5. It is 90% (or 0.90) confidence level for corresponding value of α = 0.20

Section-II
(Multiple Choice Questions)

(5 marks, 1 Mark Each)

1. Which one of these variables is a continuous random variable?
a) The time it take a randomly selected student to complete an exam
b) The number of children in a family
c) The number of women taller than 68 inches in a random sample of 5
women.
d) The number of correct guesses in a multiple-choice test.

2. A compagny manufactures batteries in batches of 13 and there is a 3%
rate of defects. Find the mean number of defects per batch.
a)
b)
c)
d)

0.4
12.6
0.39
39

3. If the z – score of normal distribution is 2.5, the mean of the distribution
is 45 and the standard deviation of normal distribution is 3 then the value
of X for a normal distribution is
a)
b)
c)
d)

97.5
47.5
52.5
67.5

4. If the sampling error (E) is allowed to increase, which of the following is
true regarding the sample size?
a)
b)
c)
d)

The sample size will increase
The sample size will decrease
The sample size will stay the same
The sample size cannot be determined

5. Use the confidence level and sample data to find a confidence interval for
estimating the population μ. Round your answer to the same number of
decimal places as the sample mean. Given: n = 105; x = 70.5; σ =
̅
6.8; 99% confidence.
a)
b)
c)
d)

9.0 < < 72.0
68.8 < < 72.2
69.2 < < 71.8
None.

Part-II (Multiple Choice Questions)
MCQ
1
2
3
4
5
Answers

Page 3 of 4

(5 marks, 1 Mark Each)

Section –III
Answer the following Essay Type Questions

(15 marks, 5 Mark Each

1. During the summer months, a rental agency keeps track of the number
of chain saws it rents each day during a given period and X denotes
the number of saws rented per day:
a) Check a probability distribution.
b) Find the mean, variance, and standard deviation for the probability
distribution.
X
0
1
2
P(x)
0.6
0.33
0.07

2. If X is binomially distributed with 5 trials and a probability of success
equal to 0.3 at each attempt.
a) What is the probability of exactly 4 successes?
b) Also find the parameter mean, variance and standard deviation?

3. Find
a) P (z < 2.37)
b) P (z > 1.82)
c) P (-1.18 < z < 2.1)