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Tpy6a [65]
2 years ago
9

Focus groups of 15 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number

(per group) who recognize the Yummy brand name is 12.5, and the standard deviation is 0.58. Would it be unusual to randomly select 15 people and find that fewer than 9 recognize the Yummy brand name?
Mathematics
1 answer:
Morgarella [4.7K]2 years ago
6 0

Answer:

Yes, 15 people would be unusual as it falls outside of 2 standard deviation of mean.

Step-by-step explanation:

Consider the provided information.

The mean number (per group) who recognize the Yummy brand name is 12.5, and the standard deviation is 0.58.

Mean = μ= 12.5  

σ = 0.58

n = 15

\mu\pm2\sigma=12.5\pm 2(0.58)\\\mu\pm2\sigma=12.5\pm1.16\\\mu\pm2\sigma=[11.34, 13.66]

Yes, 15 people would be unusual as it falls outside of 2 standard deviation of mean.

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A sociologist wishes to estimate the average number of automobile thefts in a large city per day within 2 automobiles. He wishes
anzhelika [568]

Answer:

n=(\frac{2.58(4.2)}{2})^2 =29.35 \approx 30

So the answer for this case would be n=30 rounded up to the nearest integer

Step-by-step explanation:

Information given

ME = 2 the margin of error desired

\sigma =4.2 standard deviation from previous studies

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =2 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance level is \alpha=0.01 and the critical value would be z_{\alpha/2}=2.58, replacing into formula (b) we got:

n=(\frac{2.58(4.2)}{2})^2 =29.35 \approx 30

So the answer for this case would be n=30 rounded up to the nearest integer

5 0
2 years ago
For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7
Sloan [31]

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k $

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean 210x^6y^4

We can deduce that this term will be located somewhere in the middle. So I will calculate k= 5; k=6 \text{ and } k =7.

For k=5

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just x^{n-k} y^k

For k=6

$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$

5 0
2 years ago
Harper has $15.00 to spend at her grocery store. She is going to buy bags of fruit that cost $4.75 each and one box of crackers
Andrej [43]
First write the inequality:    15\leq4.75x +3.50

Then to solve, first subtract 3.50 from both sides to get:

11.50\leq4.75x

Then divide by 4.75 to get 2.42, and since you can't buy .42 of a bag  of fruit, you round down. So your final answer would be 2 bags of fruit.
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2 years ago
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Amelia and Carmen read every night. Amelia reads the same number of pages each night. So does Carmen. The table shows the number
dmitriy555 [2]

What is the question?

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2 years ago
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Mike earns $6.50 per hour plus 4% of his sales enter an equation for mikes total earnings, e, when he works x hours and has a to
Cerrena [4.2K]
First identify what each variable means. since X is the amount of hours he works, and he makes $6.50 an hour, you know you need to multiply those two numbers together creating the 6.50x. You also know Y is his total sales, and he earns 4% of Y. To find 4% of Y you need to turn the percent into a decimal, and to do this you move the decimal two spaces to the left. Since 4 is a whole number, the decimal is after the 4 so you get .04 as your decimal. Then youd multiply .04 by Y getting .04y. Lastly you add 6.50x + .04y to get E, mikes total earnings. So your final equation is

6.50x + .04y = e

Hope this all makes sense 

3 0
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