Ms Pitts has 220 students in her class. She would like to select a systematic sample of 20 students to answer a questionnaire. She numbers the students as they enter the lecture venue i.e. the \( 1^{\text {st }} \) student to enter gets assigned the number 1 , the \( 2^{\text {nd }} \) student to enter is assigned the number 2 etc. Ms Pitts randomly selects Student 10 to be the first student in her sample. Which student is the fourth to be selected for the sample? a) Student 11 b) Student 32 c) Student 43 d) Student 20 e) Student 30

A variable \( x \) is normally distributed with mean 18 and standard deviation 4 . Round your answers to the nearest hundredth as needed. a) Determine the \( z \)-score for \( x=25 \). b) Determine the \( z \)-score for \( x=11 \). \[ z= \] c) What value of \( x \) has a \( z \)-score of 3 ? d) What value of \( x \) has a \( z \)-score of -1.5 ? e) What value of \( x \) has a \( z \)-score of 0 ? \( x=18 \)

(b) Suppose a random sample of 51 human pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of \( \overline{\mathrm{x}} \) is \( \square \) with \( \mu_{\bar{x}}=\square \) and \( \sigma_{\overline{\mathrm{x}}}=\square \). (Round to four decimal places as needed.)

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

The length of human pregnancies is approximately normal with mean \( \mu=266 \) days and standard deviation o = 16 days Complete parts (a) throug (a) What is the probability that a randomly selected pregnancy lasts less than 262 days? The probability that a randornly selected pregnancy lasts less than 262 days is approximately 0.4013 . (Round to four decimal places as needed.) Interpret this probability. Select the correct choice and fill in the answer box within your choice. (Round to the nearest integer as needed.) A. If 100 pregnant individuals were selected independently from this population, we would expect \( \square \) pregnancies to last less than 262 days B. If 100 pregnant individuals were selected independently from this population, we would expect 0 pregnancies to last exactly 262 days. C. If 100 pregnant individuals were selected independently from this population, we would expect \( \square \) pregnancies to last more than 262 days.

The length of human pregnancies is approximately nermal with mean \( \mu=206 \) days and standard deviation \( a=16 \) days. Complete parts (a) through (f). (a) What is the probability that a randomly selected pregnancy lasts less than 262 days? The probability that a randomly selected pregnaney lasts less than 262 days is approximately 0.4013 , (Round to four decimal places as needed.) Interpret this probability. Select the correct choice and fill in the answer bex within your choice. (Round to the nearest integer as needed.) A. If 100 pregnant individuals were selected independently from this population, we would expect \( \square \) pregnancies to last less than 262 days. B. If 100 pregnant individuals were selected independently from this population, we would expect \( \square \) pregnancies to last exactly 262 days.