About 7.2% of all SMC students say that they plan to transfer to a private school.  A random sample of 16 SMC students is chosen.  Find each of the following probabilities. Round each response to four decimal places.  1. What is the probability that exactly 3 of the 16 chosen students plan to transfer to a private college? [one] 2. What is the probability that more than 4 of the 16 chosen students plan to transfer to a private college. [two]

240 visitors to Yosemite National Park were polled and asked whether they were first time visitors or repeat visitors, and what their  main interest for the current visit.  The data is recorded in the table below.  Plants Animals Hiking Rock Climbing Other First-Time Visitor 27 23 31 24 9 Repeat Visitor 22 33 35 30 6 Find each of the following probabilities.  If rounding is necessary, round to three decimal places.  1. What is the probability that a randomly chosen visitor is a first-time visitor?  [a1] 2. What is the probability that a randomly chosen visitor’s main interest is hiking or they are a repeat visitor?  [a2] 3. If one visitor is randomly chosen and you know they are a repeat visitor, what is the probability that their main interest is rock climbing? [v3]

240 visitors to Yosemite National Park were polled and asked whether they were first time visitors or repeat visitors, and what their  main interest for the current visit.  The data is recorded in the table below.  Plants Animals Hiking Rock Climbing Other First-Time Visitor 27 23 25 44 9 Repeat Visitor 22 19 35 30 6 Find each of the following probabilities.  If rounding is necessary, round to three decimal places.  1. What is the probability that a randomly chosen visitor is a first-time visitor?  [a1] 2. What is the probability that a randomly chosen visitor’s main interest is hiking or they are a repeat visitor?  [a2] 3. If one visitor is randomly chosen and you know their main interest is hiking, what is the probability that they are a first time visitor? [v3]

The heights of college basketball players are normally distributed with a mean of 6.3 feet and a standard deviation of 0.2 feet.  1. If one college basketball player is randomly chosen, what is the probability that the player is less than 5.8 feet tall? Round your response to 4 decimal places. [q1] 2. 90% of college basketball players are between [lower] feet and [upper] feet tall.  (Round values to 2 decimal places.) Suppose a random sample of 40 college basketball players is randomly chosen.   3. Describe the sampling distribution of the mean for samples of size 40.  Be sure to address the shape, the mean of the sampling distribution and the standard error of the mean.  Where rounding is necessary, round to three decimal places.  The sampling distribution of the mean is [shape] with a mean of [mean] feet and standard error of [se] feet.   4. What is the probability that a random sample of 40 college basketball players results in a mean height of greater than 6.33 feet?  Complete the following to state and interpret this probability.  a. The probability is [prob].  (Round to 4 decimal places) b. if [100s] were chosen from this population, we’d expect about [number] to have a mean height greater than 6.33 feet. 

The heights of college basketball players are normally distributed with a mean of 6.3 feet and a standard deviation of 0.2 feet.  1. If one college basketball player is randomly chosen, what is the probability that the player is less than 6 feet tall? Round your response to 4 decimal places. [q1] 2. 95% of college basketball players are between [lower] feet and [upper] feet tall.  (Round values to 2 decimal places.) Suppose a random sample of 40 college basketball players is randomly chosen.   3. Describe the sampling distribution of the mean for samples of size 40.  Be sure to address the shape, the mean of the sampling distribution and the standard error of the mean.  Where rounding is necessary, round to three decimal places.  The sampling distribution of the mean is [shape] with a mean of [mean] feet and standard error of [se] feet.   4. What is the probability that a random sample of 40 college basketball players results in a mean height of greater than 6.37 feet?  Complete the following to state and interpret this probability.  a. The probability is [prob].  (Round to 4 decimal places) b. if [100s] were chosen from this population, we’d expect about [number] to have a mean height greater than 6.37 feet. 

In 2020, 15.8% of California residents were aged 65 year or older.  A random sample of 15 California residents is chosen.  Find each of the following probabilities.   Round to three decimal places.  1. What is the probability that exactly 4 in the sample are aged 65 or older?  [exact] 2. What is the probability that at most 4 in the sample are aged 65 or older?  [least]

A study is to be done to look at the proportion of SMC students that belong to a special program.  A random sample of 250 SMC students indicates that 73 of them belong to a special program.  Choose the all appropriate conditions below that confirm that the Central Limit Theorem will apply in this problem.   Only the conditions used in this class will be considered correct. 

The table below gives the probability distribution for the number of classes that a student is taking at a particular community college. Number of Classes (X) P(X) 1 0.07 2 0.11 3 0.25 4 ? 5 0.09 a. Complete the table by finding P(4), the probability that a student is taking 4 classes.  [answera] b.  Is the random variable, X, continuous or discrete?  [answerb] c. What is the most likely number of classes a student at this college is taking?  If rounding is necessary, round to two decimal places. [answerc] d. What is the expected number of classes a student at this college is taking?   If rounding is necessary, round to two decimal places.   [asnwerd] e. What is the standard deviation in the number of classes a student at this college is taking? If rounding is necessary, round to two decimal places. [answere] f. Which of the following interpretations of the expected value is correct? [exp]  

What two z-scores enclose the middle 80% of the standard normal curve?  Round to two decimal places. 

Five hundred high school students in Los Angeles were randomly chosen and classified by their GPA and how many days of school they had missed.  The data is summarized in the table below.  If rounding is necessary, round to three decimal places.    GPA < 2.0 GPA 2.0 to 3.0 GPA > 3.0 Missed 5 or fewer days 60 100 120 Missed more than 5 days 80 110 30 a. If one student is randomly chosen, what is the probability that they missed 5 days or fewer or had a GPA less than 2.0? [ans1] b. If one student is randomly chosen, what is the probability that they missed more than 5 days and had a GPA between 2.0 and 3.0? [ans2] c. If one student is randomly chosen and you know that they have missed more than 5 days, what is the probability that they had a GPA greater than 3? [ans3]