Stat Binomial 2

7/29/2019 Stat Binomial 2

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SCHOOL OF BUSINESSUAM PROF: HNVG

Normal Distribution

STATISTICS


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Finding z values


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Example 1

The weekly incomes of shift foremen in the

glass industry are normally distributed with a

mean of $1,000 and a standard deviation of

$100. What is the z value for the income X of a

foreman who earns $1,100 per week? For a

foreman who earns $900 per week?


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Example 2

As part of their quality assurance program, the Autolite

Battery Company conducts tests on battery life. For a

particular D cell alkaline battery, the mean life is 19

hours. The useful life of the battery follows a normaldistribution with a standard deviation of 1.2 hours.

1. about 68 percent of the batteries failed between what two

values?

2. About 95 percent of the batteries failed between what twovalues?

3.Virtually all of the batteries failed between what two values?


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Finding Areas under the

Normal Curve;

Probabilities


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Example 3

Recall that in example 1 we reported that the

mean weekly income of a shift foreman in the

glass industry is normally distributed with a

mean of $1,000 and a standard deviation of

$100. What is the likelihood of selecting a

foreman whose weekly income is between

$1,000 and $1,100? What is the probability of aforeman that earns $1,100 or less?


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Example 4

Refer to the information regarding the weeklyincome of the shift foremen in the glassindustry. The distribution of weekly incomes

follows the normal distribution, with a mean of$1,000 and a standard deviation of $100. What isthe probability of selecting a shift foreman in theglass industry whose income is:

Between $790 and $1,000?

Less than $790?


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Example 5

Recall the distribution of weekly incomes of

shift foremen in the glass industry; with a mean

of $1000, and a standard deviation of $100.

What is the area under this normal curve

between $840 and $1,200?


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Example 6

Using a mean of $1,000 and a standard deviation

of $100, what is the area under the normal curve

between $1,150 and $1,250?


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Example 7

A tire manufacturer wishes to set a minimum

mileage guarantee on its new MX100 tire. Tests

reveal the mean mileage is 67,900 with a

standard deviation of 2,050 miles and a normal

distribution. The manufacturer wants to set the

minimum guaranteed mileage so that no more

than 4 percent of the tires will have to bereplaced. What minimum guaranteed mileage

should the manufacturer announce?


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Finding the Z value the population

standard deviation is known The Quality Assurance Department for Cola, Inc. maintains

records regarding the amount of cola in their Jumbo bottle.The actual amount of cola in each bottle is critical, but varies asmall amount form one bottle to the next. Cola, Inc. does not

wish to underfill the bottles, because they will have a problem

with truth in labeling. On the other hand, they cannot overfilleach bottle, because they would be giving cola away, hencereducing their profits. Their records indicates that the amount ofcola follows the normal distribution. The mean amount perbottle is 31.2 ounces and the population standard deviation is 0.4

ounces. At 8 AM today the quality technician randomly selected16 bottles from the filling line. The mean amount of colacontained in the bottles is 31.38 ounces. Is this an unlikely result?Is it likely the process is putting too much soda in the bottles?

To put it another way, is the sampling error of 0.18 ouncesunusual? Select a sample of 16 bottles


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When the population mean is

unknown

The Metropolitan NY Gas Station Dealers Association

estimates that the mean number of gallons of gasoline

sold per day at a gas station is 20,000. The shape of this

distribution is unknown. A sample of 70 dealersyesterday revealed the mean number of gallons sold was

19,480. The standard deviation of the sample of 70

dealers was 4,250 gallons. Is the assertion that the

population mean is 20,000 gallons reasonable? What isthe likelihood of finding a sample with the given

statistics from the proposed population?

Stat Binomial 2

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