Book back answers and solution for Exercise questions - Maths: Probability Distributions - 1. Discrete distribution: binomial and Poisson distributions 2. Continous distribution : Poisson distributions - Miscellaneous Problems with Answer, Solution

**Miscellaneous Problems**

1. A manufacturer of metal pistons finds
that on the average, 12% of his pistons are rejected because they are either
oversize or undersize. What is the probability that a batch of 10 pistons will
contain

(a) no more than 2 rejects? (b) at least
2 rejects?

2. Hospital records show that of
patients suffering from a certain disease 75% die of it. What is the
probability that of 6 randomly selected patients, 4 will recover?

3. If electricity power failures occur
according to a Poisson distribution with an average of 3 failures every twenty
weeks, calculate the probability that there will not be more than one failure
during a particular week.

4. Vehicles pass through a junction on a
busy road at an average rate of 300 per hour.

i. Find the probability that none passes
in a given minute.

ii. What is the expected number passing
in two minutes?

5. Entry to a certain University is
determined by a national test. The scores on this test are normally distributed
with a mean of 500 and a standard deviation of 100. Raghul wants to be admitted
to this university and he knows that he must score better than at least 70% of
the students who took the test. Raghul takes the test and scores 585. Will he
be admitted to this university?

6. The time taken to assemble a car in a
certain plant is a random variable having a normal distribution of 20 hours and
a standard deviation of 2 hours. What is the probability that a car can be
assembled at this plant in a period of time .

a) less than 19.5 hours?

b) between 20 and 22 hours?

7. The annual salaries of employees in a
large company are approximately normally distributed with a mean of $50,000 and
a standard deviation of $20,000.

(a) What percent of people earn less
than $40,000?

(b) What percent of people earn between
$45,000 and $65,000?

(c) What percent of people earn more
than $70,00

8. X is a normally normally distributed
variable with mean μ = 30 and standard deviation σ = 4. Find

(a) P(x < 40)

(b) P(x > 21)

(c) P(30 < x < 35)

9. The birth weight of babies is Normally
distributed with mean 3,500g and standard deviation 500g. What is the
probability that a baby is born that weighs less than 3,100g?

People’s monthly electric bills in
chennai are normally distributed with a mean of ₹ 225 and a standard deviation
of ₹ 55. Those people spend a lot of time online. In a group of 500 customers,
how many would we expect to have a bill that is ₹ 100 or less?

**1.
(i) 0.89131 (ii) 0.34173 **

**2.
0.03295 **

**3.
0.98981**

**4.
0.0067379 or 6.7379 ×10 ^{-3} **

**5.
80.33%**

**6.
a) 0.4013 (b) 0.3413 **

**7.
a) 30.85% b) 37.20% c) 10.56%**

**8.
a) 0.9938 (b) 0.9878 (c) 0.3944 **

**9.
0.2119 **

**10.
7**

Tags : 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 : Miscellaneous Problems | with Answer, Solution | Probability Distributions

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