Answer:
<h2>135 ft²</h2><h2 />Step-by-step explanation:
see attached image
<u>shaded area = total area (1) - unshaded triangular area (2)</u>
1. area of a trapezoid = (a + b) * h/2
where a = 8, b = 18, h = 15
Area of trapezoid = (8 + 18) * 15/2 = 195 ft²
2. Area of unshaded triangle = 1/2 (8) 15 = 60 ft²
shaded area = 195 - 60 = 135 ft²
Answer:
2.28% probability that the mean amount of their monthly cell phone bills is more than $60
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 normally distributed samples are 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.
In this problem, we have that:
What is the probability that the mean amount of their monthly cell phone bills is more than $60?
This is 1 subtracted by the pvalue of Z when X = 60. So
By the Central Limit Theorem
has a pvalue of 0.9772
1 - 0.9772 = 0.0228
2.28% probability that the mean amount of their monthly cell phone bills is more than $60
