A local bakary has determined a probability distribution for the number of cheesecakes that they sell in a given day:
1 answer:
Answer:
Step-by-step explanation:
The pdf of the number of cheesecakes that they sell in a given day: by a bakery are as follows:
X 0 5 10 15 20
P 0.25 0.47 0.12 k 0.15
Use total prob =1, to find k .
k = 0.01
a) the probability of selling 15 cheesecakes in a given day = 0.01
b. What is the probability of selling at least 10 cheesecakes =P(X≥10)
= 0.28
c. the probability of selling 5 or 15 chassescakes P(5)++P(15)=0.48
d. the probaility of selling 25 cheesecakes = 0
e. Give the expected number of cheesecakes sold in a day using the discrete probability distribution?
=
f. the probability of selling at most 10 cheesecakes
=P(X≤10)
= 0.84
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Answer:
And we can use the following excel code to find the answer: "=NORM.DIST(-0.704,0,1,TRUE)"
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable of interest for a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
And we can use the following excel code to find the answer: "=NORM.DIST(-0.704,0,1,TRUE)"