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This module provides students an opportunity to practice applying concepts related to discrete distributions. This practice exercise asks students to calculate several values based on the data provided.

Student learning outcomes

  • The student will analyze the properties of a discrete distribution.

Given:

A ballet instructor is interested in knowing what percent of each year's class will continue on to the next, so that she can plan what classes to offer. Over the years,she has established the following probability distribution.

  • Let X = the number of years a student will study ballet with the teacher.
  • Let P(x) = the probability that a student will study ballet x years.

Organize the data

Complete the table below using the data provided.

x P(x) x*P(x)
1 0.10
2 0.05
3 0.10
4
5 0.30
6 0.20
7 0.10

In words, define the Random Variable X .

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On average, how many years would you expect a child to study ballet with this teacher?

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Discussion question

What does the column " P(x) " sum to and why?

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What does the column " x * P(x) " sum to and why?

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Questions & Answers

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Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ... Step 2: Find each score's deviation from the mean. ... Step 3: Square each deviation from the mean. ... Step 4: Find the sum of squares. ... Step 5: Divide the sum of squares by n – 1 or N.
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The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
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Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400 a. what is the probability of getting more than 12,000 hits? b. what is the probability of getting fewer than 9,000 hits?
Akshay Reply
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400. a. What is the probability of getting more than 12,000 hits
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1
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a= 0.20233 b=0.3384
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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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