Question
In: Statistics and Probability
he amount of pressure created from a air compressor spray is normally distributed with a mean...
he amount of pressure created from a air compressor spray is normally distributed with a mean of 10,000 pounds per square inch (PSI) and standard deviation of 800 PSI.
(1) For a random sample of n=4 sprays, what is the probability
that the sample mean will be at least 10,200 PSI?
(2) For a random sample of n=4 sprays, what is the probability that
the sample mean will be less than 9,900 PSI?
Solutions
Expert Solution
Solution: It is given that the amount of pressure created from an air compressor spray is normally distributed with a mean of 10,000 pounds per square inch (PSI) and standard deviation of 800 (PSI). Therefore, we have:
(1) For a random sample of n=4 sprays, what is the probability that the sample mean will be at least 10,200 PSI?
Answer: We are required to find:
Now using the z-score formula, we have:
Now using the standard normal table, we have:
Therefore, the probability that the sample mean will be at least 10,200 PSI is 0.3085
(2) For a random sample of n=4 sprays, what is the probability that the sample mean will be less than 9,900 PSI?
Answer: We are required to find:
Now using the z-score formula, we have:
Now using the standard normal table, we have:
Therefore, the probability that the sample mean will be less than 9,900 PSI is 0.4013
orchestra answered 1 year agoRelated Solutions
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