Struggling! Any help would be appriciated. In previous questions i was able to get all z scores but not the probability.

Question

Serum cholesterol is an important risk factor for coronary disease. Suppose that serum cholesterol is approximately normally distributed with mean 217 mg/dL and standard deviation 46.47 mg/dL. 

1. Cholesterol levels in the top 18% are classified as high enough to warrant risk for heart disease. What cholesterol level corresponds to this cut-off? 
2. z = 
3. cholesterol =  mg/dL 
4. Suppose cholesterol levels in the bottom 36% are classified as normal. What cholesterol level corresponds to a normal reading? 
5. z = 
6. cholesterol =  mg/dL
7. Between what two values do the middle 46% of cholesterol readings fall?
8. z = + 
9. between  mg/dL and  mg/dL 

Note: z-scores should include 2 decimal places; all other answers should be rounded to 3 decimal places. 

Answer 1

using z-score formula z = (x - mean)/SD, where x is cholesterol level.

first problem. Look for z-score corresponding to 82nd percentile. plug that in for z, given mean and SD, solve for x.

second problem. Look for z-score corresponding to 36th percentile. plug that in for z and solve for x.

third problem middle 46 percent is between 27 and 73 percentile (50 +/- 23). Look up z score for 73rd percentile. Because normal distribution is symmetric, z-score for 27th percentile will be the negative of the z-score for the 73rd percentile.

plug in z-score for 73rd percentile and solve for x. Same with 27th percentile. Or amount value for 73rd percentile is above the mean is the amount the value for the 27th percentile will be below it.