PELIN'S MATHEMATICS PAGE


SOLUTIONS OF THE QUESTIONS

 

1.     For x=0, the z value z=(40-30)/4=2.5

 

Hence P(x<40)=P(z<2.5) =[area of the left of 2.5]= 0.9938

 

2.     Let x be the random variable that represents the speed of cars. x has

 = 90 and = 10. We have to find the probability that x is higher than

100 or P(x > 100) 

For x = 100 , z = (100 - 90) / 10 = 1 

P(x > 90) = P(z >, 1) = [total area] - [area to the left of z = 1] 

= 1 - 0.8413 = 0.1587 

The probability that a car selected at a random has a speed greater than 100

 km/hr is equal to 0.1587

3. Let x be the random variable that represents the length of time. It has a mean of 50 and a standard deviation of 15. We have to find the probability that x is between 50 and 70 or P( 50< x < 70) 

For x = 50 , z = (50 - 50) / 15 = 0 

For x = 70 , z = (70 - 50) / 15 = 1.33 (rounded to 2 decimal places) 

P( 50< x < 70) = P( 0< z < 1.33) = [area to the left of z = 1.33] - [area to the left of z = 0] 

= 0.9082 - 0.5 = 0.4082 

The probability that John's computer has a length of time between 50 and 70 hours is equal to 0.4082.

    4. For x = 60, z = -1 

     Area to the right of z = -1 is equal to 0.8413 = 84.13% should pass the test.