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Mathematics

1 answer:

Diano4ka-milaya [45]4 years ago

8 0

There are two blue marbles so you have a 2/8 probability of drawing a blue marble on each draw since the marble is replaced after the first draw. 2/8 can be simplified to be 1/4 and then converted to be 0.25 per draw. 0.25 plus 0.25 equals 0.5. Since we are dealing with percentages multiply 0.5 x 100 which equals 50. Now take 50 and divided by the total number of marbles in the bag which is 8. 50 divided by 8 equals 6.25. So it would be about 6%.

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A marketing researcher wants to find a 96% confidence interval for the mean amount those visitors spend per person per day while

ki77a [65]

Answer:

$n=(\frac{2.054(12)}{4})^2 =37.97 \approx 38$

So then the minimum sample to ensure the condition given is n= 38

Step-by-step explanation:

Notation

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=12$ represent the population standard deviation

n represent the sample size

ME = 4 the margin of error desired

Solution to the problem

When we create a confidence interval for the mean 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 =4 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 96% of confidence interval now can be founded using the normal distribution. The significance is $\alpha=1-0.96 =0.04$ . And in excel we can use this formula to find it:"=-NORM.INV(0.02;0;1)", and we got $z_{\alpha/2}=2.054$ , replacing into formula (b) we got: