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(1) what type of probability distribution would be used to solve each problem and why;

(2) pick one problem from below and provide a detailed solution with an explanation;

(3) indicate which problem you selected to solve in your subject line.

There are three kinds of probability distributions: (1) normal probability distribution, (2) discrete probability distribution, and (3) binomial probability distribution. Normal probability distribution points to continuous probability distributions that are represented by a normal equation. Thus, if a probability is randomly distributed, then the mean, and standard deviation are determinate, and the number e and pie are constants. On the other hand, binomial probability distribution refers to the probability where n-trials result in an exact number of successes: for instance tossing a dice or a coin results in binomial probability distribution. Lastly, discrete distribution refers to probability distribution where there are countable random variables.

Considering the definitions above, question (i) and (iii) below has discrete probability distribution; question, and (ii) has binomial probability distribution.

i. The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. Find and interpret the probability that a randomly selected sixth-grade student reads less than 100 words per minute.

**Solution**

P (randomly selected sixth-grader reads less than 100 words per minute) = 0

**Explanation**

Here we consider the mean and standard deviation as the decision tools. That is, the mean is 124 words per minute while the standard deviation is 24. That implies that the fastest student reads (125 + 24) words per minute while the slowest reads (125-24) words per minute. Solving we find that the fastest sixth grader reads 149 words per minute while the slowest reads 101 words per minute. It therefore follows that there is no learner in the class that reads less than 101 words per minute. So the probability that a randomly selected student will read less than 100 words is zero.

ii. A Wendy's manager performed a study to determine a probability distribution for the number of people, X, waiting in a line during lunch. The results were as follows. Find and interpret the probability that 10 or more people are waiting in line for lunch?

iii. Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. As random sample of 20 Clarinex-D users is obtained, and the number of patients who experienced insomnia is recorded. Find and interpret probability that 3 or fewer experienced insomnia as a side effect.

September 18, 2023

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