Question

The random variable X follows a normal distribution with a mean of 10 and a standard deviation of 3.

1.

What is P(7≤X≤13)? Include 4 decimal places in your answer.

2.

What is the value of k such that P(X>k)=0.43? Include 2 decimal places in your answer.

Answer 1

Solution :

Given that ,

mean = = 10

standard deviation = = 3

P(7   x 13) =

= P[(7 - 10 / 3) (x - ) / (13 - 10 / 3) ]

= P( -1 z 1 )

= P(z 1) - P(z -1)

Using z table,

=0.8413-0.1587

=0.6826

b.

Using standard normal table,

P(Z > z) = 43%

= 1 - P(Z < z) = 0.43

= P(Z < z ) = 1 - 0.43

= P(Z < z ) = 0.57

z = 0.18 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 0.18*3+10

x= 10.54