For a birthday party Mr. Perkins or do you eat chocolate chip cookies and 16 sugar cookies each cookie is the same price he also
1 answer:
Question is not proper, Proper question is given below;
For a birthday party, Mr. Perkins orders 8 chocolate chip cookies and 16 sugar cookies. Each cookie is the same price. He also picks up a cupcake for himself, which costs $2.75. The total bill is $44.03. What is the cost of a cookie?
Answer:
The Cost of the cookie will be $1.72.
Step-by-step explanation:
Given:
Mr Perkins orders 8 chocolate chip cookies and 16 sugar cookies.
Since cost of both the cookies are same then Let us assume the cost of cookies be 'x'.
Total cost of the cookies =
Cost of Cup cakes = $2.75.
Total bill he pays = $44.03
We need to find the cost of each cookies.
Now we know that Total bill he pays is equal to sum of Cost of cookies and Cost of Cup cakes he bought.
Framing in equation form we get;
Now Subtracting both side by 2.75 using Subtraction property we get;
Now Dividing both side by 24 using Division property we get;
Hence The Cost of the cookie will be $1.72.
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Answer:
a) 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.
b) 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.
Step-by-step explanation:
To solve this question, it is important to know the Normal probability distribution and the Central Limit Theorem
Normal probability distribution
Problems of normally distributed samples can be 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
.
In this problem, we have that:
A) What is the chance HLI will find a sample mean between 5.5 and 7.1 hours?
This is the pvalue of Z when X = 7.1 subtracted by the pvalue of Z when X = 5.5.
By the Central Limit Theorem, the formula for Z is:
X = 7.1
has a pvalue of 0.9962
X = 5.5
has a pvalue of 0.0038
So there is a 0.9962 - 0.0038 = 0.9924 = 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.
B) Calculate the probability that the sample mean will be between 5.9 and 6.7 hours.
This is the pvalue of Z when X = 6.7 subtracted by the pvalue of Z when X = 5.9
X = 6.7
has a pvalue of 0.9082
X = 5.9
has a pvalue of 0.0918.
So there is a 0.9082 - 0.0918 = 0.8164 = 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.