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suppose the random variable, x, is distributed normal with mean 4 and standard deviation 1.37. suppose the probability that x is less than the value x is equal to 0.8907, that is, p(x0.8907. what is x?



Answer :

Since the probability is less than equal to 0.8907, then the value of x is 0.9750.

Given, the random variable is from of a normal distribution with

μ = 4 and  σ = 1.37

.where, μ  is the mean value and σ  is the standard deviation.

According to the Question:

P(X≤8.907) = P( X−μ/σ ≤ 0.8907 - 4.00/ 1.37)

                  = P ( Z ≤ -29196.43)

​                  

Using Z-table we get a value of x which is 0.9750

So,

P(X ≤ 0.8907) = 97.50%

According to the calculations, the required value of x is 97.50%.

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