Question

# 1. Assume that adults have IQ scores that are normally distributed with a mean of μ=100...

1. Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard deviation σ=15.

Find the probability that a randomly selected adult has an IQ less than 130.

2. Assume the readings on thermometers are normally distributed with a mean of 0 °C and a standard deviation of 1.00 °C.

Find the probability P=(−1.95<z<1.95), where z is the reading in degrees.

3. Women's heights are normally distributed with mean 63.3 in and standard deviation of 2.5 in. A social organization for tall people has a requirement that women must be at least

69 in tall. What percentage of women meet that requirement?

1)

Given,

= 100 , = 15

We convert this to standard normal as

P( X < x) = P( Z < x - / )

P( X < 130) = P( Z < 130 - 100 / 15)

= P( Z < 2 )

= 0.9772

b)

P(-1.95 < Z < 1.95) = P( Z < 1.95) - P( Z < -1.95)

= 0.9744 - ( 1 - 0.9744)

= 0.9488

c)

Given,

= 63.3 , = 2.5

We convert this to standard normal as

P( X < x) = P( Z < x - / )

P( X >= 69) = P( Z >= 69 - 63.3 / 2.5)

= P( Z >= 2.28)

= 1 - P( Z < 2.28)

= 1 - 0.9887

= 0.0113

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