Question

The times per week a student uses a lab computer are normally​ distributed, with a mean of 6.5 hours and a standard deviation of 1.5 hours. A student is randomly selected. Find the following probabilities.

​(a) Find the probability that the student uses a lab computer less than 3 hours per week.

​(b) Find the probability that the student uses a lab computer between 6 and 8 hours per week.

​(c) Find the probability that the student uses a lab computer more than 9 hours per week.

Answer 1

Solution :

Given that ,

mean =   = 6.5

standard deviation = =1.5

P(X< 3) = P[(X- ) / < (3-6.5) /1.5 ]

= P(z <-2.33 )

Using z table

=0.0099

probability=0.0099

(B)

P(6< x <8 ) = P[(6-6.5) /1.5 < (x - ) / < (8-6.5) /1.5 )]

= P( -0.33< Z <1 )

= P(Z < 1) - P(Z <-0.33 )

Using z table   

= 0.8413-0.3707

probability= 0.4706

(C)

P(x >9 ) = 1 - P(x<9 )

= 1 - P[(x -) / < (9-6.5) /1.5 ]

= 1 - P(z <1.67 )

Using z table

= 1 - 0.9525

= 0.0475

probability=0.0475