\#7 A set of data has correlation coefficient \( r \). For which value of \( r \) would the average magnitude of the residuals be the smallest? a. \( r=-0.034 \) b. \( r=0.472 \) c. \( r=0.908 \) d. \( r=0.952 \)

Find the median of the following data set. Assume the data set is a sample. \[ 38,51,34,40,44,41,41,47,46,46,45 \]

A study of 12,000 able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.11 minutes and standard deviation 0.74 minute. Choose a student at random from this group and call his time for the mile \( Y \). What is \( P(Y<6) \) ? Interpret this value. \( P(Y<6)=0.0668 \). There is about a \( 6.68 \% \) chance that the population mean is less than 6 minutes. \( P(Y<6)=0.9332 \). There is about a \( 93.32 \% \) chance that this student will run the mile in under 6 minutes. \( P(Y<6)=0.774 \). There is about a \( 77.4 \% \) chance that this student will run the mile in under 6 minutes. \( P(Y<6)=0.9332 \). There is about a \( 93.32 \% \) chance that the population mean is less than 6 minutes. \( P(Y<6)=0.0668 \). There is about a \( 6.68 \% \) chance that this student will run the mile in under 6 minutes.

Bigger animals tend to carry their young longer before birth. The length of horse pregnancies from conception to birth varies Write the event "pregnancy lasts between 325 and 345 days" in terms of \( X \). What is this probability? \( P(X<325)+P(X>345)=0.5933 \). \( P(325<X<345)=0.8996 \). \( P(325<X<345)=0.6880 \). \( P(325<X<345)=0.7425 \). \( P(X<325)+P(X>345)=0.2406 \).

From the following scenarios, choose which will likely have a negative correlation. Answer 2 Points \[ \begin{array}{l}\text { The number of parties attended per month by college students and their first-semester grades } \\ \text { The number of minutes spent on social media sites by students and their first-year GPA } \\ \text { The number of hours spent studying per week by students and their first-year GPA } \\ \text { The a dog and their daily food intake }\end{array} \]

The length of human pregnancies is approximately normal with mean \( \mu=266 \) days and standard deviation \( \sigma=16 \) days (a) What is the probability that a randomly selected pregnancy lasts less than 262 days? The probability that a randomly selected pregnancy lasts less than 262 days is approximately (Round to four decimal places as needed.)