Complete question:
The manager of a supermarket would like to determine the amount of time that customers wait in a check-out line. He randomly selects 45 customers and records the amount of time from the moment they stand in the back of a line until the moment the cashier scans their first item. He calculates the mean and standard deviation of this sample to be barx = 4.2 minutes and s = 2.0 minutes. If appropriate, find a 90% confidence interval for the true mean time (in minutes) that customers at this supermarket wait in a check-out line
Answer:
(3.699, 4.701)
Step-by-step explanation:
Given:
Sample size, n = 45
Sample mean, x' = 4.2
Standard deviation
= 2.0
Required:
Find a 90% CI for true mean time
First find standard error using the formula:




Standard error = 0.298
Degrees of freedom, df = n - 1 = 45 - 1 = 44
To find t at 90% CI,df = 44:
Level of Significance α= 100% - 90% = 10% = 0.10

Find margin of error using the formula:
M.E = S.E * t
M.E = 0.298 * 1.6802
M.E = 0.500938 ≈ 0.5009
Margin of error = 0.5009
Thus, 90% CI = sample mean ± Margin of error
Lower limit = 4.2 - 0.5009 = 3.699
Upper limit = 4.2 + 0.5009 = 4.7009 ≈ 4.701
Confidence Interval = (3.699, 4.701)
Set this up as a proportion.
400/15 = x/6
Solve for x.
I just hope to help! :)
Measures of angles 2, 3, 4, added equal 180
One of the unknown angles (let's called it n) has a complement (meaning their sum adds up to 90 degrees) and the other angle is 8 times the unknown angle (8n)
With all this information, you should have the equation:
n + 8n = 90
To solve, combine like terms to get:
9n = 90
Divide by 9 on both sides to isolate the variable n.
n = 10
Now we plug back in to find our angle measurements. The first angle, n, is 10 degrees. The second angle, 8n, is 8 * 10 which is 80; the second angle is 80 degrees.
Hi there! :)
<u>Answer:</u>
In order to maintain the same ratio, she should sell 18 band posters.
<u>Step-by-step explanation:</u>
<u>Initial ratio:</u>
Ratio is: 105 movie posters for 90 band posters = <u>105 : 90</u>
She sells 21 movie posters, which means that we are left with 105 movies minus the 21 she sold.
105 - 21 = 84 → She now has <u>84</u> movie posters.
In order to answer your question, you'll need to use the cross product method:
105 movie posters → 90 band posters
84 movie posters → X
<u>(90 × 84)</u> ÷ 105 = X
<u>7,560 ÷ 105</u> = X
72 = X ⇒ Number of band posters she should have left to maintain the same ratio.
She has 90 band posters :
90 <u>- X</u> = 72
Add "X" to each side of the equation → 72 + X = 72 + X
90 = <u>72</u> + X
Subtract 72 from each side of the equation → 90 - 72 = 18
<u>18 = X</u>
There you go! I really hope this helped, if there's anything just let me know! :)