Maria wanted to know if there was a connection between her coffee consumption and how well she slept that night. For weeks, Mari
a recorded how many cups of coffee she drank in the morning and how many hours she slept that night.
What is the probability that a randomly selected day is one when she slept exactly 7 hours given that the day is one when she drank exactly 1 cup of coffee? (serious answers only please)
A. 3/15
B. 3/10
C. 7/15
D. 7/10
What is the probability that a randomly selected day is one when she slept exactly 7 hours given that the day is one when she drank exactly 1 cup of coffee? (serious answers only please)
A. 3/15
B. 3/10
C. 7/15
D. 7/10
1 answer:
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Answer:
And we can find this probability using the complement rule:
And using the normal standard distirbution table or excel we got:
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 that represent the variable if interest of a population, and for this case we know the distribution for X is given by:
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 using the complement rule:
And using the normal standard distirbution table or excel we got: