Question

For a normal distribution with a mean of u = 60 and a standard deviation of...

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.

Homework Answers

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

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