Write an algebraic expression for “12 less than the quotient of 12 and a number z.”
1 answer:
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Answer:
90% confidence interval for the true population mean textbook weight is [35.79 ounces , 38.21 ounces].
Step-by-step explanation:
We are given that you measure 50 textbooks' weights, and find they have a mean weight of 37 ounces.
Assume the population standard deviation is 5.2 ounces.
Firstly, the Pivotal quantity for 90% confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample mean weight = 37 ounces
= population standard deviation = 5.2 ounces
n = sample of textbooks = 50
= true population mean textbook weight
<em>Here for constructing 90% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>
<u></u>
<u>So, 90% confidence interval for the population mean, </u><u> is ;</u>
P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5%
level of significance are -1.645 & 1.645}
P(-1.645 < < 1.645) = 0.90
P( <
<
) = 0.90
P( <
<
) = 0.90
<u>90% confidence interval for</u> = [
,
]
= [ ,
]
= [35.79 , 38.21]
Therefore, 90% confidence interval for the true population mean textbook weight is [35.79 ounces , 38.21 ounces].