Question

Q: 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 between 84 and 116.
• Draw two normal curves, one over the other, where the top curve is for xvalues and the bottom curve is for z-values.
• What is the z-score for x = 84?
• What is the z-score for x = 116?
• Shade the region of the curves that represents the desired probability and
label the appropriate values on the horizontal axes of the curves.
• Use the normal distribution tables to find 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 between 84 and 116.
• Draw two normal curves, one over the other, where the top curve is for xvalues and the bottom curve is for z-values.
• What is the z-score for x = 84?
• What is the z-score for x = 116?
• Shade the region of the curves that represents the desired probability and
label the appropriate values on the horizontal axes of the curves.
• Use the attached normal distribution tables to find the probabilty

Answer 1

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

Now the probability that a randomly selected adult has an IQ between X1 = 84 and X2 = 116 is calculated by finding the Z scores at X values which are calculated as:

Now the probability is computed as:

=> P(−0.9333 ≤ Z≤ 1.0667)

=Pr(Z≤1.0667)−Pr(Z≤−0.9333)

Thus the probability is computed using the excel formula for normal distribution which is =NORM.S.DIST(1.067, TRUE)-NORM.S.DIST(-0.933, TRUE), thus the probability is computed as:

=0.8569−0.1753

=0.6816

The normal cuve for x values is plotted as:

The normal curve fo Z scores is plotted as:

Now the probability between the scores is plotted as:

The Z table is :