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Chapter 5: Q 5.145. (page 231)

Equipment breakdowns: A factory manager collected data on the number of equipment breakdown per day. From those data she derived the probability distribution shown in the following table, Where W denote the number of breakdown on a given day.

Part (a) Determine 渭wand蟽w, Round your answer for the standard deviation to three decimal places.

Part (b) On average, how many breakdown occur per day?

Part (c) About how many breakdown are expected during a 1 year period assuming 250 work days per year?

Short Answer

Expert verified

Part (a) 渭w=0.25and蟽w=0.526

Part (b) 0.25

Part (c) 62.5

Step by step solution

01

Part (a) Step 1. Given information. 

Consider the following data table:

w012
P(W = w)0.800.150.05
02

Part (a) Step 2.μ and  σ are the values.

The random variable W's mean is:

渭w=鈭�w路P(W=w)渭w=(0脳0.080)+(1脳0.15)+(2脳0.05)渭w=0+0.15+0.10渭w=0.25

The random variable W's standard deviation is;

蟽w=鈭�w路P(W=w)-渭2蟽w=(02脳0.080)+(12脳0.15)+(22脳0.05)-0.252蟽w=0+0.15+0.20-0.0625蟽w=0.536

03

Part (b) Step 1. On average, there are a number of breakdowns every day.

The mean value =0.25 comes from section a.

The average number of breakdowns per day is equivalent to the mean value.

As a results, The average number of breakdowns per day is 0.25.

04

Part (b) Step 1.The anticipated number of breakdowns over a one-year period

The number of working days in a calendar year = 240

The expected number of breakdowns;

渭W脳250=0.25(250)=62.5

As a result, number of breakdowns over a one-year period = 62.5

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Most popular questions from this chapter

Suppose that a simple random sample is taken from a finite population in which each member is classified as either having or not having a specified attribute. Fill in the following blanks.

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