Mathematics, 29.08.2019 01:30 nina288

If cynthia is in the 95th percentile and the mean of her test scores is 180 with a standard deviation of 15, which of the following scores would cynthia most likely get on a standardized test?
a. 205
b. 171
c. 220
d. 300
this is for apex
?

Answers: 1

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This is a confidence interval problem where we are looking for the number from the given options which falls inside the upper 95% confidence interval.

A confidence interval is a range of values so defined that there is a specified probability that the value of a parameter lies within it.

Here, we are to find a range of values so defined that there is a 95% probability that the value of Cynthia's standardized test score lies within it.

The 95% confidence interval of the mean is given by
$\bar{x}\pm1.96\left( \frac{\sigma}{ \sqrt{n} } \right)$
where: $\bar{x}$ is the sample mean, 1.96 is the standard normal score associated with 95%, $\sigma$ is the standard deviation and n is the sample size.

Since, the sample size is unknown, we reduce the formular to
$\bar{x}\pm1.96(\sigma)$

Therefore, the 95% confidence interval is
$180\pm1.96(15)=180\pm29.4$

Now, since we are interested with the upper confidence, we have that the value of Cynthia's test score is between 180 and 180 + 29.4, i.e. between 180 and 209.4

Therefore, from the options given the score that Cynthia would most likely get on a standardized test is 205.

Answer from: Quest

the answer is 200

step-by-step explanation:

this is a problem about poisson probabilities. i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.

here's how you can see a poisson distribution coming. when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution. this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot. there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything. the form of the distribution is

probability of n chips = {[e^(-x)]*(x^n)} / (n! )

Answer from: Quest

b mark me branliest thx

step-by-step explanation:

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