57. Suppose 22% of students at a certain university are out-of-state students. A professor takes random sample of 50 students. Let X = the number of out-of-state students in the sample. (a) How many students are expected to be out-of-state? By how much does this vary? (b) What is the probability that 10 will be out-of-state?lloms om atersbuds to UP (c) What is the probability that 10 or fewer will be out-of-state? T (d) What is the probability that fewer than 10 will be out-of-state? gati

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I need help with question 57 and 58
**Educational Content: Probability and Statistics Problems**

**Problem 57: Out-of-State Students**

Suppose 22% of students at a certain university are out-of-state students. A professor takes a random sample of 50 students. Let \( X \) = the number of out-of-state students in the sample.

- **(a)** How many students are expected to be out-of-state? By how much does this vary?
- **(b)** What is the probability that 10 will be out-of-state?
- **(c)** What is the probability that 10 or fewer will be out-of-state?
- **(d)** What is the probability that fewer than 10 will be out-of-state?

**Problem 58: Left-Handed Baseball Players**

About 10% of the general population is left-handed. However, about 25% of baseball players are left-handed. Suppose we take a random sample of 30 baseball players and let \( X \) = the number of left-handed players in the sample.

- **(a)** What is the probability that at most 8 are left-handed?
- **(b)** What is the probability that 8 are left-handed?
- **(c)** What is the probability that more than 12 are left-handed?
- **(d)** What is the probability that at least 12 are left-handed?
Transcribed Image Text:**Educational Content: Probability and Statistics Problems** **Problem 57: Out-of-State Students** Suppose 22% of students at a certain university are out-of-state students. A professor takes a random sample of 50 students. Let \( X \) = the number of out-of-state students in the sample. - **(a)** How many students are expected to be out-of-state? By how much does this vary? - **(b)** What is the probability that 10 will be out-of-state? - **(c)** What is the probability that 10 or fewer will be out-of-state? - **(d)** What is the probability that fewer than 10 will be out-of-state? **Problem 58: Left-Handed Baseball Players** About 10% of the general population is left-handed. However, about 25% of baseball players are left-handed. Suppose we take a random sample of 30 baseball players and let \( X \) = the number of left-handed players in the sample. - **(a)** What is the probability that at most 8 are left-handed? - **(b)** What is the probability that 8 are left-handed? - **(c)** What is the probability that more than 12 are left-handed? - **(d)** What is the probability that at least 12 are left-handed?
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