Assume that women’s heights are normally distributed with a mean given by µ =

64.6 inches and standard deviation given by σ = 2.2 inches. What area under the normal curve corresponds to the probability that a woman’s height is between 63.7 inches and
64.7 inches?

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z scores.

Thanks,

Jacky

To find the area under the normal curve corresponding to the probability that a woman's height is between 63.7 inches and 64.7 inches, we can use the concept of the standard normal distribution.

1. Convert the given values to z-scores:
The formula for calculating the z-score is: z = (x - µ) / σ
For the lower bound, 63.7 inches, the z-score is:
z1 = (63.7 - 64.6) / 2.2
For the upper bound, 64.7 inches, the z-score is:
z2 = (64.7 - 64.6) / 2.2

2. Look up corresponding probabilities:
Next, we need to find the probabilities associated with these z-scores. We can use a standard normal distribution table or a calculator to find the probabilities given the z-scores.

3. Calculate the area:
To find the area between the two z-scores, subtract the probability corresponding to the lower z-score from the probability corresponding to the upper z-score:
Area = P(z1 ≤ Z ≤ z2)

For example, if the probability corresponding to z1 is 0.307 and the probability corresponding to z2 is 0.366, the area between the two z-scores would be:
Area = 0.366 - 0.307 = 0.059

Therefore, the area under the normal curve corresponding to the probability that a woman's height is between 63.7 inches and 64.7 inches is 0.059.