X denotes a binomial random variable with parameters n and p. For each exercise, indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.

Khaleesi Herbert
2021-09-08
Answered

X denotes a binomial random variable with parameters n and p. For each exercise, indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.

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Viktor Wiley

Answered 2021-09-09
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At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of 40 freshmen sharing a common lounge area. How many international students would you expect to find in a typical cluster? With what standard deviation?

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Calculate probability within both binomially distributed and normally distributed random variables.

Calculate probability within both binomially distributed and normally distributed random variables.

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Students arrive for the much dreaded JEE Advanced according to a Poisson process with rate lambda. For sanitization process they must stand in a queue,each student can take different time or same time compared with some other student for sanitization. Let us denote the time taken by i-th student as $X}_{i$ .

$X}_{i$ are independent identically distributed random variables. We assume that $X}_{i$ takes integer values in range 1,2, ... , n, with probabilities $p}_{1},{p}_{2},\dots ,{p}_{n$ . Find the PMF for $N}_{t$ , the number of students in sanitization queue at time t.

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According to a 2020 article, 69% of men do not wash their hands after using a public restroom. Suppose a random sample of 40 men are selected. What is the probability that exactly 30 will not wash their hands after using a public restroom?

1) 0.839

2) 0.221

3) 0.102

4) 0.358

1) 0.839

2) 0.221

3) 0.102

4) 0.358

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Assume that a procedure yields a binomial distribution with

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The probability of rain on any given day in a region is found to be 0.1 based on the Binomial probability distribution.

a) What is the probability of 4 days with rain in one week?

b) What is the probability that it will rain in the next 4 days?

c) What is the probability that it will rain 4 consecutive days after 3 days with no rain in one week?

a) What is the probability of 4 days with rain in one week?

b) What is the probability that it will rain in the next 4 days?

c) What is the probability that it will rain 4 consecutive days after 3 days with no rain in one week?

asked 2021-12-13

Can a binomial random variable X have a mean $=7$ and the variance $=11$ . Why or why not?