# Probability density function for random variable

The weekly demand X for copies of a popular word processing program at a computer store has the following probability distribution shown here.

X: 0 1 2 3 4 5

Px(x): .06 .14 .16 .14 .12 .10

X: 6 7 8 9 10

Px(x): .08 .07 .06 .04 .03

What is the probability that three or more copies of the program will be demanded in a particular week?

What is the probability that the demand will be for at least two but no more than six?

The store policy is to have eight copies of the program available at the beginning of every week. What is the probability that the demand will exceed the supply in a given week?

2. The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?

© BrainMass Inc. brainmass.com October 16, 2018, 8:49 am ad1c9bdddf - https://brainmass.com/statistics/probability-density-function/probability-density-function-random-variable-149257#### Solution Preview

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The weekly demand X for copies of a popular word processing program at a computer store has the following probability distribution shown here.

x P(X=x)

0 0.06

1 0.14

2 0.16

3 0.14

4 0.12

5 0.1

6 0.08

7 0.07

8 0.06

9 0.04

10 0.03

What is the probability that three or more copies of the program will be demanded in a particular week?

Here we need P(X ≥3) = 0.14+0.12+0.10+0.08+0.07+0.06+0.04+0.03 =0.64

What is the probability that the demand will be for at least two but no more than six?

Here we need ...

#### Solution Summary

This solution gives the step by step method for computing probability density function for random variable.