Book back answers and solution for Exercise questions - Maths: Probability Distributions: Continuous distribtuion : Normal Distribution: Problem Questions with Answer, Solution

**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?

**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**

Tags : Problem Questions with Answer, Solution | Probability Distributions , 12th Business Maths and Statistics : Chapter 7 : Probability Distributions

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12th Business Maths and Statistics : Chapter 7 : Probability Distributions : Exercise 7.3: Normal Distribution | Problem Questions with Answer, Solution | Probability Distributions

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