6.1.2 Use the empirical rule to determine values at 1, 2, and 3 standard deviations from the mean.

6.2.1 Calculate normal distribution probabilities using technology.

Newborn Babies & Tuition Rates

1. According to kidshealth.org, newborn babies typically sleep between 14-17 hours in a 24-hour period. Let's assume that sleep times are normally distributed with a mean of 15.5 hours and a standard deviation of 0.5 hours. Use the empirical rule to answer the following questions. Draw and shade a normal distribution to support your answer.

1. What percent of babies get between 15.5 hours and 16 hours of sleep?

1. What percent of babies get between 14.5 hours and 16 hours of sleep?

1. What percent of babies get more than 16 hours of sleep?

1. How many hours of sleep would a baby need to get to be in the top 2.5% of sleep times?

1. What percentage of babies get between 15 and 16.25 hours of sleep? You may wish to convert to z-scores and use this Desmos calculator page to determine the percentage. https://www.desmos.com/calculator/5ubvhyrip7

2) Super heavy pumpkins are showcased each year at the state fair. These pumpkins have

weights that are normally distributed with a mean weight of 15.1 kilograms and a

standard deviation of 2.2 kilograms. What is the approximate percent of all super heavy pumpkins that weigh between 13.0 kilograms and 16.5 kilograms? Explain using the empirical rule why an answer of 75% is not reasonable.

3) How are tuition rates distributed among private colleges in Pennsylvania? The data here

(Tuition) was obtained from https://www.collegetuitioncompare.com. Schools that did not list acceptance rates (which were primarily technical and trade schools) were removed from the data set.

1. Calculate the mean and standard deviation for the data set.

NOTE: This can be done by typing the commands average(C2:C113) and stdev(C2:C113) in a cell of the spreadsheet.

1. If the distribution of tuition was approximately normal, what would be the range for the middle 68% of tuition rates?

1. If the distribution of tuition was approximately normal, what would be the range for the middle 95% of tuition rates?

1. If the distribution of tuition was approximately normal, what would be the range for the middle 99.7% of tuition rates?

1. What percent of the distribution is within 1 standard deviation?

1. What percent of the distribution is within 2 standard deviations?

1. What percent of the distribution is within 3 standard deviations?

1. Based on your results to the previous questions, do you think tuition at private colleges in Pennsylvania are normally distributed? Explain.

1. Go to the Desmos Calculator page at www.desmos.com/calculator/zmuhx8wgnj and click on the circles in front of lines 3 & 4. Explain how the histogram of the distribution and the normal distribution shown support your answer to the previous question.