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

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STATISTICS

Total PointsTrue/False

____/5

MCQ

____/5

Short Answer

____/15

Total

____/25

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STATISTICS (STAT-101)

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

Section-IState whether the following statements are True or False. (5 marks, 1 MarkEach)1. Mean value over an infinite number of observations of the variables is theexpected 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 arelikely 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 examb) The number of children in a familyc) The number of women taller than 68 inches in a random sample of 5women.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)

0.412.60.3939

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

97.547.552.567.5

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

The sample size will increaseThe sample size will decreaseThe sample size will stay the sameThe sample size cannot be determined

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

d)

9.0 < < 72.068.8 < < 72.269.2 < < 71.8None.

Part-II (Multiple Choice Questions)MCQ12345Answers

Page 3 of 4

(5 marks, 1 Mark Each)

Section –IIIAnswer the following Essay Type Questions

(15 marks, 5 Mark Each

1. During the summer months, a rental agency keeps track of the numberof chain saws it rents each day during a given period and X denotesthe number of saws rented per day:a) Check a probability distribution.b) Find the mean, variance, and standard deviation for the probabilitydistribution.X012P(x)0.60.330.07

2. If X is binomially distributed with 5 trials and a probability of successequal 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. Finda) P (z < 2.37)b) P (z > 1.82)c) P (-1.18 < z < 2.1)