claytonhopkins
12.02.2020 •
Mathematics
The random variable x has a normal distribution with standard deviation 25. It is known that the probability that x exceeds 150 is .90. Find the mean
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Ответ:
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 of a population, and for this case we know the distribution for X is given by:
Where and
We know the following condition:
For this case we can use the z score formula given by:
And we can find a z score that accumulates 0.9 of the area on the left and 0.1 on the right and this value is:
Becuase P(Z<-1.28) =0.1 and P(Z>-1.28) = 0.9
So then if we use the z score formula we got:
And if we solve for the mean we got:
Ответ:
red is spelled Step-by-step explanation: lster :]