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In: Statistics and Probability

The average clothes washer uses 15 gallons of water per load, with a standard deviation of...

The average clothes washer uses 15 gallons of water per load, with a standard deviation of 3.0 gallons. What is the probability that a random sample of 30 loads will provide a sample mean within one half gallon of the population mean?

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Expert Solution

Solution :

Given that ,

mean = = 15

standard deviation = = 3.0

n = 30

= = 15

= / n = 3.0 / 30

P(14.5 < < 15.5)  

= P[(14.5 - 15) / 3.0 / 30 < ( - ) / < (15.5 - 15) / 3.0 / 30)]

= P(-0.91 < Z < 0.91)

= P(Z < 0.91) - P(Z < -0.91)

Using z table,  

= 0.8186 - 0.1814  

= 0.6372

orchestra answered 2 years ago
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