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olga_2 [115]
3 years ago
14

You took a random sample of 12 two-slice toasters and found the mean price was $61.12 and the standard deviation was $24.62. Con

struct a 95% confidence interval for the population mean. Assume the prices are normally distributed.
Mathematics
1 answer:
Minchanka [31]3 years ago
5 0

Answer:

Step-by-step explanation:

We want to determine a 95% confidence interval for the population mean for the prices of slice toasters.

Number of sample, n = 12

Mean, u = $61.12

Standard deviation, s = $24.62

For a confidence level of 95%, the corresponding z value is 1.96.

We will apply the formula

Confidence interval

= mean ± z ×standard deviation/√n

It becomes

61.12 ± 1.96 × 24.62/√12

= 61.12 ± 1.96 × 7.107

= 61.12 ± 13.93

The lower end of the confidence interval is 61.12 - 13.93 =47.19

The upper end of the confidence interval is 61.12 + 13.93 = 75.05

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Alright, first thing's first, simplify the equation as much as you can. If you wanted, I suppose you could just multiply everything by 40, but that's super unconventional.

7x/8 - 3x/8 = 1/5 + 3/10

Simplify:
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Make sure that when subtracting or adding fractions that the denominators (The number on the bottom of the fraction) are equal.

In order to add 1/5 and 3/10 together, all we have to do is ensure that both denominators are equal.

To do this, simply multiply 1/5 by 2/2. The new fraction will be 2/10 (You can do this since it's the exact same fraction, 2/10 will simplify down to 1/5. The reason we did this was to make sure that the two fractions had equal denominators).

Our equation now looks like this:
4x/8 = 2/10 + 3/10

Add the fractions on the right:
4x/8 = 5/10

Huh, whaddya know? Both the fraction on the left and the right can be simplified into 1/2! (4/8 becomes 1/2, and 5/10 becomes 1/2)

1x/2 = 1/2
x/2 = 1/2

If you want to, I suppose you could cross multiply to check, but the answer's already pretty obvious.

x = 1

Good luck! If you need me to explain anything I did here, just ask :))
-T.B.
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