The average height of Susan's 8th grade class is 56 Inches. However, the height of any student in the class can vary by up to 4
Inches
from the average. Which Inequality shows all thepossible heights (h) for any given student in the class?
from the average. Which Inequality shows all thepossible heights (h) for any given student in the class?
1 answer:
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Step 1: Assign variable for the unknown that we need to find.
Let ' x ' be the number of miles traveled by Jacob so far (His distance from starting point)
Step 2: Use the sentence given to set up an equation
Sentence 1: "His distance from his starting point was exactly 100 miles more than three times the distance remaining until the finishing point"
Total distance is 2800 miles, if his distance from the starting point is 'x', then remaining distance can be represented by 2800 - x.
Using the sentence we can write the below equation...
Distributing 3 in the right side of the equation, we get...
Adding 3x on both sides of the equation, we get...
Combine like terms in the left side of the equation, we get...
Dividing 4 on both sides of the equation, we get...
Simplifying the fraction on either side of the equation, we get...
Conclusion:
Out of the 2800 miles, Jacob travelled a distance of 2125 miles and remaining miles that he need to cover will be <u>675 miles</u>.
Answer:
a) 18.94% probability that the sample mean amount purchased is at least 12 gallons
b) 81.06% probability that the total amount of gasoline purchased is at most 600 gallons.
c) The approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers is 621.5 gallons.
Step-by-step explanation:
To solve this question, we use 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.
For sums, we can apply the theorem, with mean and standard deviation
In this problem, we have that:
a. In a sample of 50 randomly selected customers, what is the approximate probability that the sample mean amount purchased is at least 12 gallons?
Here we have
This probability is 1 subtracted by the pvalue of Z when X = 12.
By the Central Limit theorem
has a pvalue of 0.8106.
1 - 0.8106 = 0.1894
18.94% probability that the sample mean amount purchased is at least 12 gallons
b. In a sample of 50 randomly selected customers, what is the approximate probability that the total amount of gasoline purchased is at most 600 gallons.
For sums, so
This probability is the pvalue of Z when X = 600. So
has a pvalue of 0.8106.
81.06% probability that the total amount of gasoline purchased is at most 600 gallons.
c. What is the approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers.
This is X when Z has a pvalue of 0.95. So it is X when Z = 1.645.
The approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers is 621.5 gallons.