The hypotenuse is 82 centimeters long.
En la granja hay 509 puercos anota el número antecesor y el número sucesor de la cantidad.
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The hypotenuse is 82 centimeters long.
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.
You can break large numbers into a sum of a multiple(s) of 10 and the last digit of the number. For example, you can break 26 as 20+6, or 157 as 100+50+7.
Then, using the distributive property, you can turn the original multiplication into a sum of easier multiplications. For example, suppose we want to multiply 26 and 37. This is quite challenging to do in your mind, but you can break the numbers as we said above:
All these multiplications are rather easy, because they either involve multiples of 10 of single-digit numbers:
Answer:
Growth when: b>1.
Decay when: 0<b<1.
Step-by-step explanation:
Any function in the form , where a > 0, b > 0 and b not equal to 1 is called an exponential function with base b.
if 0 < b < 1. It is an example of an exponential decay.
The general shape of an exponential with b > 1 is an example of exponential growth.
Hence,
An exponential function is expressed in the form The relation represents a growth when b >1 and a decay when 0<b<1.