Question

Please show your answer and a draw the graphs.

A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling at more than 100 km/hr?

For a certain type of computers, the length of time bewteen charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours.

Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Tom takes the test and scores 585. Will he be admitted to this university?

Answer 1

Solution :

Given that ,

mean = = 90

standard deviation = = 10

P(x >100 ) = 1 - P(x <100 )

= 1 - P[(x- ) / < (100 - 90) /10 ]

= 1 - P(z <1 )

Using z table,    

= 1 - 0.8413

=0.1587

(B)

Solution :

Given that ,

mean = = 50

standard deviation = = 15

P(50<x <70 ) = P[(50 - 50) /15 < (x - ) / < (70 - 50) /15 )]

= P( 0< Z <1.33 )

= P(Z <1.33 ) - P(Z <0 )

Using z table,  

=0.9082-0.5

=0.4082

(C)

Given that,

mean = = 500

standard deviation = = 100

Using standard normal table,

P(Z > z) = 70%

= 1 - P(Z < z) = 0.70

= P(Z < z ) = 1 - 0. 70

= P(Z < z ) = 0.30

= P(Z < -0.52) = 0.30

z = -0.52

Using z-score formula  

x = z * +

x= -0.52 *100+500

x= 448

yes admitted to this university