The distribution of weights of adult males in a certain county is strongly right-skewed with a mean weight of 185 lbs and standard deviation 16 lbs. What is the probability that a simple random sample of 100 adult males from this county has a mean weight between 172 and 188 lbs

0.962 = 96.2% probability that a simple random sample of 100 adult males from this county has a mean weight between 172 and 188 lbs.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

The distribution of weights of adult males in a certain county is strongly right-skewed with a mean weight of 185 lbs and standard deviation 16 lbs.

This means that

Sample of 100:

This means that

What is the probability that a simple random sample of 100 adult males from this county has a mean weight between 172 and 188 lbs?

This is the p-value of Z when X = 188 subtracted by the p-value of Z when X = 172. So

X = 188

By the Central Limit Theorem

has a p-value of 0.9620

X = 172

has a p-value of 0.

0.9620 - 0 = 0.962

0.962 = 96.2% probability that a simple random sample of 100 adult males from this county has a mean weight between 172 and 188 lbs.

find out the value of b

step-by-step explanation:

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.