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Sec. 5.3 โ Normal Distribution: Finding Values Instead of finding an area or probability using the normal curve, you can also do the reverse: find a z-score given the probability or area. Find the z-score that corresponds to a cumulative area of 0.3632. Find the z-score that has 10.75% of the distributionโs area to its right. Find the z-score that corresponds to the given percentile, decile or quartile. ๐5 ๐3 ๐ท3 ๐57 You can rewrite the z-score formula and solve for x. This will allow you to give an x-value for a given z-score. Remember: ๐ง = Therefore, ๐ฅ = The speeds of vehicles along a stretch of highway are normally distributed, with a mean of 67 miles per hour and a standard deviation of 4 miles per hour. Find the speeds ๐ฅ corresponding to z-scores of 1.96, -2.33, and 0. Interpret your results. Scores for a civil service exam are normally distributed, with a mean of 75 and a standard deviation of 6.5. To be eligible for civil service employment, you must score in the top 5%. What is the lowest score you can earn and still be eligible for employment? In a randomly selected sample of 1169 men ages 35-55, the mean total cholesterol level was 210 milligrams per deciliter with a standard deviation of 38.6 milligrams per deciliter. Assume the total cholesterol levels are normally distributed. Find the highest total cholesterol level a man in the 35-55 age group can have and be in the lowest 1%.