Question

Asked Nov 15, 2019

4 views

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.6 ppm and standard deviation 1.4 ppm. 17 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.

What is the distribution of

X

X

?

X

X

~ N(,)

What is the distribution of

¯

x

x¯

?

¯

x

x¯

~ N(,)

What is the probability that one randomly selected city's waterway will have less than 8.5 ppm pollutants?

For the 17 cities, find the probability that the average amount of pollutants is less than 8.5 ppm.

For part d), is the assumption that the distribution is normal necessary? YesNo

Step 1

It is given that the amount of pollutants follows normal distribution with mean 8.6 and standard deviation 1.4.

That is, µ= 8.6, σ = 1.4.

Thus, **X~ N (8.6,1.4).**

Step 2

**Central Limit Theorem for mean:**

If a random sample of size *n *is taken from a population having mean µ and standard deviation σ then, as the sample size increases, the sample mean approaches the normal distribution with mean µ and standard deviation σ/sqrt(n).

**Finding the distribution of X-bar:**

It is given that, *μ* = 8.6 and σ = 1.4. * *

Random samples of 17 (*n*) cities is considered.

By central limit theorem for mean, the average amount of pollutants follows a normal distribution with mean μ = 8.6 and standard deviation 1.4/sqrt (17) = 0.3395.

Thus, the distribution of **X-bar ~ N(8.6,0.3395).**

Step 3

**Finding the probability that the amount of pollutants in a randomly selected city is less than 8.5:**

Denote the random variable *X* as the amount of pollutants in a randomly selec...

Tagged in

Q: nsurance claim amounts follow a normal distribution with a mean of $800 and a known standard deviati...

A: From the given information, mean (μ) =$800 and standard deviation (σ) =$300And also sample size (n) ...

Q: The probability that an observation taken from a standard normal population will have a z greater th...

A: From the standard normal distribution table, the probability that an observation taken from a standa...

Q: 3. A psychologist theorized that people could hear better when they have just eaten a large meal. Si...

A: Two sample t-test:Two sample t-test is used to test the difference between two population means. A c...

Q: Normal distribution problem: Mean = 10; SD = 2; X=8, X=12 A farmer believes that the yields of his t...

A: The provided information are:

Q: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit...

A: Standard normal distribution:The standard normal distribution is a special case of normal distributi...

Q: Blackjack, or twenty-one as it is frequently called, is a popular gambling game played in Las Vegas ...

A: (a)The probability that both cards dealt are aces or 10-point cards is obtained below:The probabilit...

Q: Need the answer to question 10.

A: Given that,Population mean = $48000Population standard deviation = $9000

Q: 15O

A: According to the radio program, the fictional town has all the children who are above average.

Q: 7 part a, b, and c

A: Here, denote µ1, µ2, µ3, µ4 as mean number of problems solved by the four groups.