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) =

=

=

=

=

Here, is obtained by using standard normal table(Area under normal curve). In Area under normal curve we have to see row 0.4 under column 0.00

= 0.0228 In Area under normal curve we have to see row -2.0 under column 0.00

= 0.6554 - 0.0228

= 0.6326.

Hence, P(600 ≤ X < 660) = 0.6326.

Step3 of 3:

b).

P(|X −650| ≤ c) = 0.9544

= 0.9544

= 0.9544

= 0.9772

We have to see where 0.9772 falls in standard normal table(area under normal table).

In area under normal table 0.9772 falls in row 2.0 under column 0.00

Hence,

= 50

Therefore, c = 50.

Conclusion:

Therefore,

a).P(600 ≤ X < 660) = 0.6326.

b). c = 50.