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# Normal Distribution Starter Quiz 1

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Question 1

Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean –1 and variance unknown. If P(X ≤ -1) = P(Y ≥ 2), the standard deviation of Y is

Question 2

A sample of size 45 is drawn from a slightly skewed distribution. What is the approximate shape of the sampling distribution?

Question 3

It was found that the LED bulb’s has a mean lifetime of hours and a standard deviation of hours. Three of such bulbs are connected so that when one burns out, another will go on. Assuming the lifetimes are normally distributed, what is the probability that lighting will take place for at least 5000 hours:

(Given Data:

a. Area under Normal curve between z=0 to 1.92 is 0.4726

b. Area under Normal curve to the right of is 0.3749

c. Area under Normal curve to the left of is 0.2704)

Question 4

The area (in percentage) under standard normal distribution curve of random variable Z within limits from -1 to 1 is…..

Question 5

Which of the following option is correct for moment generating function for Normal distribution function defined as ?

Question 6

The normal distribution N(μ, σ2) with mean μ and variance σ2 > 0 has probability distribution function:

N(x| μ, σ2) = for x R

The difference of median and mean is ________.

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