A large retirement community has a current population more than 5,000 residents. The distribution of ages of all residents is left skewed with a mean of 65.5 years and a standard deviation of 12.5 year. Suppose you are to conduct a survey and take a random sample of 100 residents of the community. Which of the following corretly describe how to find the probability that you obtain a sample mean age that is younger than 64 years? a) Find the area to the left of z = -0.12 under a standard normal curve. b) Find the area to the right of z = -1.2 under a standard normal curve. c) Find the area to the left of z = -1.2 under a standard normal curve. d) Find the area to the right of z = -0.12 under a standard normal curve. e) None of above

c) Find the area to the left of z = -1.2 under a standard normal curve.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probabiliy distribution

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X, or the area to the left of Z in the normal curve. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, which is the area to the right of Z in the normal curve.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation , the sample means with size n of at least 30 can be approximated to a normal distribution with mean and standard deviation

In this problem, we have that:

Which of the following corretly describe how to find the probability that you obtain a sample mean age that is younger than 64 years?

Area to the left of z when X = 64 under the standard normal curve. We have to find Z.

Applying the Central Limit Theorem

So the correct answer is:

c) Find the area to the left of z = -1.2 under a standard normal curve.

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

ruth is 6 years old

step-by-step explanation:

6 + 24 = 30,   so 6/30 = .2  

if you do 1/5 it also equals .2, so that is the answer.