Mars Candy claims that 10% of all M&Ms are blue. Assume that the M&Ms in a 1 pound bag form an SRS from all M&Ms. The particular bag we examine contains 320 M&Ms. What is the probability that the bag we selected
contains more than 12% blue M&Ms?

0.1170 = 11.70% probability that the bag we selected contains more than 12% blue M&Ms.

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation

Mars Candy claims that 10% of all M&Ms are blue.

This means that

The particular bag we examine contains 320 M&Ms.

This means that

Mean and standard deviation:

What is the probability that the bag we selected contains more than 12% blue M&Ms?

This is 1 subtracted by the pvalue of Z when X = 0.12. So

By the Central Limit Theorem

has a pvalue of 0.8830

1 - 0.8830 = 0.1170

0.1170 = 11.70% probability that the bag we selected contains more than 12% blue M&Ms.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.