Answer: Real world problem is "A student have c toffee he distribute th part of those toffees to his friends. He gave total 21 toffees to his friend".
Explanation:
Let a student have c number of toffees in his bag.
It is given that he distribute th part of those toffees to his friends.
The th part of c toffees is,
The total number of distributed toffees is 21.
It is the same as given equation.
If we change the equation in words it means the th part of a number c is 21.
Answer:
a) 79.67% probability that a randomly selected bottle has at least 355 ml
b) 99.29% probability that the bottles of a randomly selected 6-pack of beer have an average of at least 355 ml.
c) 88.88% probability that the total amount of beer in the 6-pack is less than 2131.5 ml
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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 question:
a. What is the probability that a randomly selected bottle has at least 355 ml?
This is 1 subtracted by the pvalue of Z when X = 355. So
has a pvalue of 0.2033
1 - 0.2033 = 0.7967
79.67% probability that a randomly selected bottle has at least 355 ml.
b. What is the probability that the bottles of a randomly selected 6-pack of beer have an average of at least 355 ml?
Now
By the Central Limit Theorem
has a pvalue of 0.0071
1 - 0.0071 = 0.9929
99.29% probability that the bottles of a randomly selected 6-pack of beer have an average of at least 355 ml.
c. What is the probability that the total amount of beer in the 6-pack is less than 2131.5 ml?
2131.5/6 = 355.25
This is the pvalue of Z when X = 355.25.
has a pvalue of 0.1112
1 - 0.1112 = 0.8888
88.88% probability that the total amount of beer in the 6-pack is less than 2131.5 ml
The first line shown in choice A is which means "the first term is -2"
The next line in choice A means "the nth term () is found by multiplying the prior term (
) by 8". Put another way: multiply each term by 8 to get the next term.
first term = -2
second term = 8*(first term) = 8*(-2) = -16
third term = 8*(second term) = 8*(-16) = -128
fourth term = 8*(third term) = 8*(-128) = -1024
and so on.