Answer:
The smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income is 48.
Step-by-step explanation:
The complete question is:
The mean salary of people living in a certain city is $37,500 with a standard deviation of $2,103. A sample of n people will be selected at random from those living in the city. Find the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income. Round your answer up to the next largest whole number.
Solution:
The (1 - <em>α</em>)% confidence interval for population mean is:
The margin of error for this interval is:
The critical value of <em>z</em> for 90% confidence level is:
<em>z</em> = 1.645
Compute the required sample size as follows:
![n=[\frac{z_{\alpha/2}\cdot\sigma}{MOE}]^{2}\\\\=[\frac{1.645\times 2103}{500}]^{2}\\\\=47.8707620769\\\\\approx 48](https://tex.z-dn.net/?f=n%3D%5B%5Cfrac%7Bz_%7B%5Calpha%2F2%7D%5Ccdot%5Csigma%7D%7BMOE%7D%5D%5E%7B2%7D%5C%5C%5C%5C%3D%5B%5Cfrac%7B1.645%5Ctimes%202103%7D%7B500%7D%5D%5E%7B2%7D%5C%5C%5C%5C%3D47.8707620769%5C%5C%5C%5C%5Capprox%2048)
Thus, the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income is 48.
Answer:
96
Step-by-step explanation:
12 times 4 gets you 48
48 times 2 gets you 96
Answer:
69
70.5
84
Step-by-step explanation:
Firstly, we need to sort this list of numbers in order to perform calculations on it.
To find the mean we must add up and divide by the amount of numbers there are.
To find the median we must find the number in the middle of the set.
As there are two numbers in the middle positions, 69 and 72.
We must take the average of these two numbers to determine the middle.
The most is the most common number, which is 84.
Answer:
Y= x + 1
I really hope this helps you
Answer:
Answers below
Step-by-step explanation:
a. The question is asking how many number of groups that contain of equal balls from both red and blue can be formed, which are none because one of the groups will have one more excess red ball. b. The facts that are given are that there are 27 red balls and 18 blue balls. c. Solve it by making an equation and statements with the facts given to make the most fit answer for this problem. d. The total number of balls he has is 45 consisting of 18 blue and 27 red. e. The largest and most equal amount of balls is 9 blue and 13 balls in one pile, 9 blue and 14 in the other. Hope this helps! (Sorry if I couldn't answer everything)
