Answer:
The 95% confidence interval for the population mean is between $140.89 and $159.11.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 150 - 9.11 = $140.89
The upper end of the interval is the sample mean added to M. So it is 150 + 9.11 = $159.11
The 95% confidence interval for the population mean is between $140.89 and $159.11.
B is 3, m is 0.75 x is number of miles
Answer:
286.5 days.
Step-by-step explanation:
This is a normal distribution problem with
Mean = μ = 266 days
Standard deviation = σ = 16 days.
Let the number that corresponds to the top 10% be a.
P(x > a) = 0.1
Let the z-score of a be z'
z' = (x - μ)/σ = (a - 266)/16
Using the normal distribution table, we can obtain the z-score that corresponds to z'
P(x > a) = P(z > z') = 1 - P(z ≤ z') = 0.1
P(z ≤ z') = 1 - 0.1 = 0.9
From the tables, z' = 1.282
P(z ≤ 1.282) = 0.9
And P(z > 1.282) = 0.1
1.282 = (a - 266)/16
16 × 1.282 = a - 266
20.512 = a - 266
a = 286.512 days
Hope this Helps!!!