The sum of 3 numbers is 62. The first number can be represented by the variable x. The second number is 7 more than the first nu
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Answer:
A 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].
Step-by-step explanation:
We are given that x is normally distributed with a known standard deviation of 12.6.
A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample average mean response = 9 hours
= population standard deviation = 12.6
n = sample of legal professionals = 250
= mean number of hours a legal professional works
<em>Here for constructing a 95% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.</em>
<u>So, 95% confidence interval for the population mean, </u><u> is ;</u>
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u>95% confidence interval for</u> = [
,
]
= [ ,
]
= [7.44 hours, 10.56 hours]
Therefore, a 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].