If X is N(650, 625), find

(a) P(600 ≤ X < 660).

(b) A constant c > 0 such that P(|X −650| ≤ c) = 0.9544.

Solution 7E

Step1 of 3:

We have We have random variable X which follows normal distribution with mean 650 and variance 625.

That is

= 25.

We need to find,

(a) P(600 ≤ X < 660).

(b) A constant c > 0 such that P(|X −650| ≤ c) = 0.9544.

Step2 of 3:

Let “X” be random variable which follows normal distribution with parameters .

That is X N()

X N[625]

The probability mass function of normal distribution is given by

,

Where,

= mean of X

= variance

= standard deviation.

a).

P(600 ≤ X < 660) =

= ...