Packaging: A variety of packing solutions exist for products that must be kept within a specific temperature range.  Cold chain distribution is particularly useful in the food and pharmaceutical industries.  A packaging company strives to maintain a constant temperature for its packages.  It is believed that the temperature for its packages follows and normal distribution with a mean of 5 degrees Celsius and a standard deviation of 0.3 degrees Celsius.  Inspectors take weekly samples for 5 weeks of eight randomly selected boxes and report the temperature in degrees Celsius.  The data is given below: Week 1 Week 2 Week 3 Week 4 Week 5 3.98 5.52 5.79 3.98 5.14 4.99 5.52 6.42 5.79 6.25 5.15 4.98 4.88 5.77 4.89 5.23 4.28 4.02 4.3 5.99 4.77 5.12 4.76 6.41 6.35 5.21 5.08 5.08 4.55 5.11 5.51 5.86 4.58 6.02 6.02 4.95 4.95 5.44 5.95 4.28   Construct an x̅ chart.  Plot the five weekly sample means on the x̅   chart.

In nutrition, the recommended daily allowance of vitamins is a number set by the government to guide an individual's daily vitamin intake. Actually, vitamin needs vary drastically from person to person, but the needs are closely approximated by a normal curve. To calculate the recommended daily allowance, the government first finds the standard deviation and the average need for vitamins among people in the population. The recommended daily allowance is then defined as the mean plus 2.7 times the standard deviation. What fraction of the population will receive adequate amounts of vitamins under this plan? Click here to see page 1 of the table for areas under the standard normal curve. Click here to see page 2 of the table for areas under the standard normal curve. The fraction of the population that will receive adequate amounts of vitamins under the given plan is (Type an integer or decimal rounded to the nearest thousandth as needed.)

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 68 miles per​ hour, with a standard deviation of 3 miles per hour. Estimate the percent of vehicles whose speeds are between 65 miles per hour and 71 miles per hour.​ (Assume the data set has a​ bell-shaped distribution.) Approximately nothing​% of vehicles travel between 65 miles per hour and 71 miles per hour.

Human body temperatures for healthy individuals have approximately a normal distribution with mean 98.25 °F and standard deviation .75 °F. (The past accepted value of 98.6 Fahrenheit was obtained by converting the Celsius value of 370, which is correct to the nearest integer.) a. Find the 90th percentile of the distribution. b. Find the 5th percentile of the distribution. c. What temperature separates the coolest 25% from the others?

A parenting magazine reports that the average amount of wireless data used by teenagers each month is 5 Gb. For her science fair project, Ella sets out to prove the magazine wrong. She claims that the mean among teenagers in her area is less than reported. Ella collects information from a simple random sample of 25 teenagers at her high school, and calculates a mean of 4.7 Gb per month with a standard deviation of 0.9 Gb per month. Assume that the population distribution is approximately normal. Test Ella's claim at the 0.01 level of significance. Step 3 of 3: Draw a conclusion and interpret the decision. E Tables E Keypad Answer Keyboard Shortcuts We reject the null hypothesis and conclude that there is sufficient evidence at a 0.01 level of significance that the average amount of wireless data used by teenagers each month is less than 5 Gb. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.01 level of significance that the average amount of…

Willow Road and Arroyo Seco are schools in different states. The heights of students at Willow Road have a population mean of 50.4 inches and a standard deviation of 6 inches. The heights of students at Arroyo Seco have a population mean of 54.3 inches with a standard deviation of 2.3 inches. For each school, the distribution of the heights of students is clearly bell-shaped.Elsa is a student at Willow Road and is 67 inches tall. Jane is a student at Arroyo Seco and is 59 inches tall.

A parenting magazine reports that the average amount of wireless data used by teenagers each month is 10 Gb. For her science fair project, Ella sets out to prove the magazine wrong. She claims that the mean among teenagers in her area is less than reported. Ella collects information from a simple random sample of 16 teenagers at her high school, and calculates a mean of 9.1 Gb per month with a standard deviation of 1.3 Gb per month. Assume that the population distribution is approximately normal. Test Ella's claim at the 0.05 level of significance. Step 3 of 3: Draw a conclusion and interpret the decision.