Question

For a normal distribution with a mean of u = 60 and a standard deviation of o = 10,

find the proportion of the population corresponding to each of the following.

a. Scores greater than 65.

b. Scores less than 68.

c. Scores between 50 and 70.

Answer 1

Solution :

Given that ,

mean = = 60

standard deviation = = 10

a) P(x > 65) = 1 - p( x< 65)

=1- p P[(x - ) / < (65 - 60) / 10]

=1- P(z < 0.5)

Using z table,

= 1 - 0.6915

= 0.3085

b) P(x < 68) = P[(x - ) / < (68 - 60) /10 ]

= P(z < 0.8)

Using z table,

= 0.7881

c) P(50 < x < 70) = P[(50 - 60)/10 ) < (x - ) /  < (70 - 60) / 10) ]

= P(-1 < z < 1)

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

Using z table,

= 0.8413 - 0.1587

= 0.6826