Question

In: Statistics and Probability

Suppose that the random variable X is normally distributed with standard deviation sigma =4. If the probability that...

Suppose that the random variable X is normally distributed with standard deviation sigma =4. If
the probability that X between 20 and the mean mu is 0.3944,
(a) Find mu .

(b) What value of X is such that only %33 of the values are above it?

(c) If a sample of size 16 is taken at random from the above distribution, what is the probability that it has an average greater than 26?

Expert Solution

Let ,

(a) We have ,

...........(I)

From standard normal distribution table,

...............(II)

From (I) and (II) , we get ,

Therefore ,

(b) We have ,

...........(I)

From standard normal distribution table,

...............(II)

From (I) and (II) , we get ,

Therefore , x=16.76

(c) Now ,

Therefore , the probability that it has an average greater than 26 is approximately 0

orchestra answered 2 years ago

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