Question

Let x denote the IQ for an individual selected at random from a certain population. The value of x must be a whole number. Suppose that the distribution of x can be approximated by a normal distribution with mean value 95 and standard deviation 15. Approximate the probabilities below. (Round all answers to four decimal places.)(a) P(x = 95) =Incorrect: Your answer is incorrect.(b) P(x ? 105) =(c) P(x < 105) = (Hint: x < 105 is the same as x ? 104.)(d) P(75 ? x ? 115) =

Answer 1

a)0.0266

b)0.2742

c)0.7257

d)0.6668

Explanation:

If x is normally distributed with mean value of 95 and standard deviation of 15. We can approximate

a) the mass probability:

P(x = 95) = 0.0266

b)
`P(x \geq 105) = 1 - P(x < 105) = 1 - P(x \leq 104) = 1 - 0.7257 = 0.2742`

c)
`P(x < 105) = P(x \leq 104) = 0.7257`

d)
`P(75 \leq x \leq 105) = P(x \leq 105) - P(74 \leq x) = 0.7475 - 0.0807 = 0.6668`