A researcher wants to estimate the mean serum cholesterol level for college age women.  In a past study the standard deviation for this measure was 42 units.  If the researcher wants to be off in his estimate by no more than three units (with 99% confidence), how large must his sample be?

If a person’s z score equals 1.61, what percentage of the observations are more extreme?

It is often quoted that in a normal distribution, 95% of the data lies 1.96 deviations either side of the mean. How many deviations from the mean would 88 percent lie?

Neil scored 67 on his calculus class final and was devastated by his failing grade. His class distribution had a mean of 54 and a standard deviation of 7. Greg was quite proud of his score of 88 for his Spanish language class. His class distribution had a mean of 97 with a standard deviation of 6. Who did better relative to their class?

The biologist wants to estimate the average age of Coyotes in Tuolumne County. Her estimates from past experience suggest the standard deviation is 1.3 years. How big of a sample should she take to be 95% sure his estimate is off by no more than 3minutes?

If a person’s z-score equalas 2.08, what is their percentile? Thank you.

This looks like another problem. Read carefully. Sergio is doing a long hike and is carefully calculating his pack weight. An energy bar has mean weight 1.71 ounces and standard deviation 0.037. The weights of the bars are independent. A juice box has mean weight 7.1 ounces and standard deviation 0.25. The weights of the juice boxes are independent.  If he takes 3 energy bars and 5 juice boxes, what will be the MEAN of the total weight in pounds from these items? Hint: If W is the weight in ounces, then W/16 is the weight in pounds.

There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores is approximately Normal with mean = 21.5 and standard deviation = 5.4. SAT Scores are reported on a scale from 600 to 2400. The distribution of SAT scores is approximately Normal with mean = 1498 and standard deviation = 316. (b) Joshua scores 17 on the ACT. Anthony scores 1030 on the SAT. Assuming both tests measure the same thing, who has the higher score? Report both z-scores. (c) What is the purpose of finding the z-scores for both the ACT and SAT scores?

Adrianna is trying to figure out the sample size for the data set she wants to collect. She thinks the population standard deviation could be as low as 120 or as high as 136. Explain to Adrianna the impact standard deviation will have on her sample size.