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Ira Lisetskai [31]
3 years ago
7

A store owner is interested in opening a second shop. She wants to estimate the true average daily revenue of her current shop t

o decide whether expanding her business is a good idea. The store owner takes a random sample of 60 days over a six-month period and finds that the mean revenue of those days is 3,472.00 dollars with variance 315,900.20 square dollars. Calculate a 95% confidence interval to estimate the true average daily revenue.
Mathematics
1 answer:
Alex3 years ago
6 0
Every confidence interval has associated z value. As confidence interval increases so do the z value associated with it. 
The confidence interval can be calculated using following formula:
\overline{x} \pm \frac{zs}{\sqrt n}
Where \overline{x} is the mean value, z is the associated z value, s is the standard deviation and n is the number of samples.
We know that standard deviation is simply a square root of variance:
s=\sqrt{315900.20}=\$562.05
The confidence interval of 95% has associated z value of <span>1.960.
</span>Now we can calculate the confidence interval for our income:
3472.00\pm \frac{1.960\cdot 562.05}{\sqrt{60}}\\ \$3472.00\pm142.22


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A consumer organization estimates that over a​ 1-year period 20​% of cars will need to be repaired​ once, 5​% will need repairs​
gtnhenbr [62]

Answer:

a) 0.5476

b) 0.0676

c) 0.4524

Step-by-step explanation:

Given this information, we can conclude that 74% of the cars won't need any repairs over a 1-year period (100 - 20 - 5 - 1 = 74%). And 26% will need at least 1 repair over a 1-year period.

P(car doesn't need repair) = 0.74

P (car needs repair) = 0.26

If you own two cars, the probability that:

<u>a) Neither will need repair:</u>

We need that car 1 won't need repair AND car 2 won't need repair.

=P(Car 1 doesn't need repair) x P(Car 2 doesn't need repair)

= 0.74 x 0.74 = 0.5476

The probability that neither will need repair is 0.5476.

<u>b) Both will need repair:</u>

We need that car 1 needs repair AND car 2 needs repair.

P(Car 1 needs repair) x P(Car 2 needs repair)

= 0.26 x 0.26 = 0.0676

The probability that both will need repair is 0.0676

<u>c) At least one car will need repair</u>

Car 1 needs repair or Car 2 needs repair or both need repair.

To solve this one, it's easier to use the complement of P(neither needs repair)

1 - P(neither needs repair)

1 - (0.74)(0.74)  = 1 - 0.5476 = 0.4524

The probability that at least one car will need repair is 0.4524

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3 years ago
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Answer:

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Step-by-step explanation:

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You are running a concession stand at a basketball game. You are selling hotdogs and sodas. Each hotdog cost $1.50 and each soda
Lubov Fominskaja [6]

Answer:

35 hotdogs

Step-by-step explanation:

You are running a concession stand at a basketball game. You are selling hotdogs and sodas.

Let the number of hot dogs be represented by x

The number of soda be represented by y

You sold a total of 87 hotdogs and sodas combined

x + y = 87

x = 87 - y

Each hotdog cost $1.50 and each soda cost $0.50. At the end of the night you made a total of $78.50.

Hence we have the equation:

$1.50 × x + $0.50 × y = $78.50

1.50x + 0.50y = 78.50

Substitute 87 - y for x

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How many hotdogs did you sell?

Using the equation:

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x = 35 hotdogs

Hence, you sold 35 hotdogs

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