20. Some researchers claim that herbal supplements such as ginseng or ginkgo biloba enhance human memory. To test this claim, a researcher selects a sample of \( n=25 \) college students. Each student is given a ginkgo biloba supplement daily for 6 weeks and then all of the participants are given a standardized memory test. Scores on the normalized test are \( \mu=70 \) and standard deviation of 15 . The sample of 25 students had a mean score of \( M=75 \). (8 points) a. Do the data indicate a significant effect of the herb on memory? Use a two-tailed test with \( \alpha=0.05 \). (Show all steps.)

Which of the following statements are TRUE about the Normal Distribution? Check all that apply. The graph of the Normal Distribution is bell-shaped, with tapering tails that never actually touch the horizontal axis. \( 50 \% \) of the data values lie at or above the mean. about \( 95 \% \) of all data values lie within 1 standard deviation of the mean. The mean, median and mode are all equal and occur at the center of the distribution. Data values are spread evenly around the mean. Data values farther from the mean are less common than data values closer to the mean.

A set of exam scores is normally distributed with a mean \( =74 \) and standard deviation \( =8 \). \( 95 \% \) of the data values lie between 58 \( \% \) of the exam scores are between 66 and 74 . \( \% \) of the exam scores are between 74 and 90 . \( \% \) of the exam scores are between 82 and 90 . \% oxam scores are greater than or equal to 66 .

A variable \( x \) is normally distributed with mean 21 and standard deviation 5. a) Determine the \( z \)-score for \( x=27 \). b) Determine the \( z \)-score for \( x=15 \). c) What value of \( x \) has a \( z \)-score of 1.8 ? \( x=x= \) d) What value of \( x \) has a \( z \)-score of -0.6 ? e) What value of \( x \) has a \( z \)-score of 0 ? \( x= \)

1.3.1 Bereken die gemiddelde aantal huishoudings in Suid-Afrika wat gedurende 2022 nie toegang tot die internet gehad het nie.

A variable is normally distributed with mean 18 and standard deviation 9 . Use your graphing calculator to find each of the following areas. Write your answers in decimal form. Round to the nearest thousandth as needed. a) Find the area to the left of 17.