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Answer:
a
$10,151 $11448.12
b
Step-by-step explanation:
From the question we are told that
The sample size is n = 19
The sample mean is $10,800
The standard deviation is $1095
The population mean is $225
Given that the confidence level is 99% the level of significance is mathematically represented as
%
=>
Now the critical values of is obtained from the normal distribution table as
The reason we are obtaining values for is because
is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while
is the area under the normal distribution curve for just one tail and we need the value for one tail in order to calculate the confidence interval
Now the margin of error is obtained as
substituting values
The 99% confidence interval for the population mean yearly premium is mathematically represented as
substituting values
$10,151 $11448.12
The largest sample needed is mathematically evaluated as
substituting values