Exercise 7.3: Normal Distribution

Exercise 7.3

1. Define Normal distribution.

2. Define Standard normal variate.

3. Write down the conditions in which the Normal distribution is a limiting case of binomial distribution.

4. Write down any five chief characteristics of Normal probability curve.

5. In a test on 2,000 electric bulbs, it was found that bulbs of a particular make, was normally distributed with an average life of 2,040 hours and standard deviation of 60 hours. Estimate the number of bulbs likely to burn for (i) more than 2,150 hours (ii) less than 1,950 hours (iii) more 1,920 hours but less than 2,100 hours.

6. In a distribution 30% of the items are under 50 and 10% are over 86. Find the mean and standard deviation of the distribution.

7. X is normally distributed with mean 12 and sd 4. Find P(X ≤ 20) and P(0 ≤ X ≤ 12)

8. If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches , how many students have height (a) greater than 72 inches (b) less than or equal to 64 inches (c) between 65 and 71 inches.

9. In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take less than 16.35 seconds to develop prints.

10. Time taken by a construction company to construct a flyover is a normal variate with mean 400 labour days and standard deviation of 100 labour days. If the company promises to construct the flyover in 450 days or less and agree to pay a penalty of  ₹10,000 for each labour day spent in excess of 450. What is the probability that

(i) the company pays a penalty of atleast ₹ 2,00,000?

(ii) the company takes at most 500 days to complete the flyover?

Answers:

5. (i) 67 (ii) 134 (iii) 1637 

6. (i) mean = 60.48 (ii) standard deviation = 19.78

7. (i) 0.9772 (ii) 0.49865 

8. (a) 46 (b) 46 (c) 342

9. 0.719 10. (i) 0.2420 (ii) 0.8413