Billy and Tommy are playing a dice game with a six-sided die. Billy needs to roll a 3 or higher to win the game. What is the pro
1 answer:
Answer:
0.667 is the probability that Billy will roll a 3 or higher.
Step-by-step explanation:
We are given the following in the question:
E: Rolling of a six-sided die
The sample space for the given event is
S: {1, 2, 3, 4, 5, 6}
We have to find the probability that Billy will roll a 3 or higher.
P( roll a 3 or higher) =
Thus, 0.667 is the probability that Billy will roll a 3 or higher.
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Answer:
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 weights of ripened peaches grown in the southeastern United States of a population, and for this case we know the distribution for X is given by:
Where and
For this case we want to find the interquartile range. From definition the IQR is a measure of dispersion defined as:
Where Q3 represent the 3 quartile and Q1 the first quartile. We need to find these values.
For this Q1 we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 25% of data from the top 75% is 5.6608.
For this Q3 we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25
If we use condition (b) from previous we have this
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 75% of data from the top 25% is 6.7392.
And then the