### Department of Mathematics and Statistics

Department of Mathematics and Statistics

This is an assignment for stats. I highly believe it can be done within 1 page or 1 and a ?half. This assignment is worth only 3 per cent, therefore, I do not want to spend much. Please have a look and let me know

MEMORIAL UNIVERSITY OF NEWFOUNDLAND

Department of Mathematics and Statistics

Assignment #2 STAT 2500-001 W19 Due on Tuesday, Feb. 12, 5:00pm

1. The probability distribution is

x -1 0 1 2 3

p(x) 0.2 0.15 0.25 0.3 0.1

Compute the expected value and the variance of the random variable. (10)

2. A study revealed that 70% of students from heavy-smoking families showed signs of nasal allergies on physical exams. Consider a sample of 25 students exposed daily to heavy smoking. (15)

(a) What is the probability that fewer than 20 of the students will have nasal allergies?

(b) What is the probability that more than 15 of the students will have nasal allergies?

(c) On average,how many of the 25 students would you expect to show signs of nasal allergies?

3. Use results from an output you obtained from the R software. Suppose x is a binomial random variable. Find the following probabilities: (15)

(a) P(x = 5) for n = 10, p = 0.3

(b) P(8 < x < 18) for n = 20, p = 0.7

(c) P(x < 7) for n = 20, p = 0.6

4. Use results from an output you obtained from the R software. Suppose x is a normal random variable. Find the following probabilities: (15)

(a) P(x = 5) for µ = 5, s = 0.3

(b) P(8 < x < 18) for µ = 15, s = 5

(c) P(x < 7) for µ = 5, s = 1

5. The length of time it takes MUN students to find a parking spot around St. John’s campus follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected student will take between 1 and 3 minutes to find a parking spot on campus. (15)

6. A fair coin is tossed 100 times. What is the probability of observing at least 55 heads

P(x=55)? (Approximate the binomial distribution with a normal distribution) (15)

1

7. The board of examiners that administers the real estate broker’s examination in a certain

state found that the mean score on the test was 490 and the standard deviation was 72.

If the board wants to set the passing score so that only the best 10% of all applicants pass, what is the passing score? Assume that the scores are normally distributed. (15)

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