The fuel consumption, in miles per gallon, of all cars of a particular model has a...

The fuel consumption, in miles per gallon, of all cars of a particular model has a mean of 25 and a standard deviation of 2. The population distribution can be assumed as normal. A random sample of these cars is taken.

a. Find the probability that the sample mean fuel consumption will be fewer than 24 miles per gallon if (i) a sample of 1 observation is taken, (ii) a sample of 4 observations if taken and (iii) a sample of 16 observations is taken.

b. Explain why the three answers in part a. differ in the way they do. Draw a graph to illustrate your reasoning.

Solutions

Expert Solution

is the graph of part a(i). when n=1

is the graph of part a (ii) when n=4

is the graph of part a (iii) when n=16.

Note the z scores decreases as we increase the sample size keeping other conditions same.

Hence, such a change in probability happens in these 3 cases.

The graphs are provided for the same event of

P(<24) for n=1,4,16.

If there is any understanding problem regarding this please feel free to ask any doubt in comment box. Thank you.

orchestra answered 1 year ago

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