Answer:
99% confidence interval for the mean number of toys purchased each year is [7.6 , 7.8].
Step-by-step explanation:
We are given that a toy manufacturer wants to know how many new toys children buy each year. A sample of 1417 children was taken to study their purchasing habits.
Also, the population standard deviation is 1.8.
So, the pivotal quantity for 99% confidence interval for the average age is given by;
P.Q. = ~ N(0,1)
where, = sample mean = 7.7
= population standard deviation = 1.8
n = sample of children = 1417
= population mean
<em>So, 99% confidence interval for the population mean, </em><em> is ;</em>
P(-2.5758 < N(0,1) < 2.5758) = 0.99
P(-2.5758 < < 2.5758) = 0.99
P( < < ) = 0.99
P( < < ) = 0.99
<u>99% confidence interval for </u> = [ , ]
= [ , ]
= [7.6 , 7.8]
Therefore, 99% confidence interval for the mean number of toys purchased each year is [7.6 , 7.8].