Question
In: Statistics and Probability
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 2 years agoRelated Solutions
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