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

Question

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

in progress 0
2 weeks 2022-01-07T08:33:18+00:00 2 Answers 0 views 0

Step-by-step explanation:

In the attachment 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: 