A garden shop sells top soil that is sold by

1

A garden shop sells top soil that is sold by the cubic yard. When a customer buys a cubic yard a front loader is used to scoop the top soil from the storage bin and transfer it to the customers truck; thus the amount transferred to the truck is an approximation. On average the weight of the top soil transferred to a truck is 2,150 lbs. with a standard deviation of 19 lbs. The weight is normally distributed.

What is the probability that a customer receives over 2200 lbs. of top soil?

Round your answer to the ten-thousandths place.

________

2

A garden shop sells top soil that is sold by the cubic yard. When a customer buys a cubic yard a front loader is used to scoop the top soil from the storage bin and transfer it to the customers truck; thus the amount transferred to the truck is an approximation. On average the weight of the top soil transferred to a truck is 2,150 lbs. with a standard deviation of 19 lbs. The weight is normally distributed.

In a single day, top soil is sold to eight customers. What is the probability that the average weight sold is less than 2,130 lbs.?

Round your answer to the ten-thousandths place.

________

3

The average pH level of the water in a Lake is 6.11 with a standard deviation of 0.53. Consider the pH distribution of averages from samples of size 20 from the lake. What is the standard deviation for the sampling distribution created from averages of 20?

Round to the nearest hundredths place.

________

4

Let the random variable X be uniformly distributed such that X is any real number between 0 and 14. Consider the distribution of sample averages of three numbers from this distribution. Which is the correct statement about the distribution of the random variable X?

Question options:

A) The distribution of X-bar is is uniform.

B) The distribution of X-bar is normal.

C) The distribution of X-bar is approximately normal.

D) None of the mentioned choices.

5

Let the random variable X be uniformly distributed such that X is any real number between 0 and 14. Consider the distribution of sample averages of twenty numbers from this distribution. Which is the correct statement about the distribution of the random variable X?

Question options:

A) The distribution of X-bar is uniform.

B) The distribution of X-bar is normal.

C) The distribution of X-bar is approximately normal.

D) None of the mentioned choices.