Question

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. For a randomly selected adult, find the probability. Round scores to nearest whole number.

1.) Prob. of IQ less than 85

2.)Prob. of IQ greater than 70

3.) Prob. of randomly selected adult having IQ between 90 and 110.

Answer 1

Solution :

(a)

P(x < 85) = P[(x - ) / < (85 - 100) / 15]

= P(z < -1)

= 0.1587

(b)

P(x > 70) = 1 - P(x < 70)

= 1 - P[(x - ) / < (70 - 100) / 15]  

= 1 - P(z < -2)

= 0.9772

(c)

P(90 < x < 110) = P[(90 - 100)/ 15) < (x - ) /  < (110 - 100) / 15) ]

= P(-0.67 < z < 0.67)

= P(z < 0.67) - P(z < -0.67)

= 0.4971