Assume the random variable x is normally distributed with mean mu equals 50μ=50 and standard deviation sigma equals 7σ=7. compute the probability. be sure to draw a normal curve with the area corresponding to the probability shaded. upper p left parenthesis upper x greater than 41 right parenthesisp(x> 41) which of the follow

P(X>41) = 0.9015 or 90.15%

Step-by-step explanation:

We have a mean and a standard deviation .

To answer the probability P(X>41), or the probability that in a Normal Distribution, with mean and standard deviation , we have values greater than 41.

We use here values for the standardized normal curve, for which, we know that the z variable describes a Normal Distribution with mean and standard deviation .

Having

The value z = 1.2857 corresponds to a cumulative probability of 0.4015 (approximately). But we are interested in z = -1.2857.

Since the Normal Distribution is symmetrical, the z-score of 0.4015 indicates the distance from the population mean (the value is 0.4015 units from the mean).

Then, we have to subtract that value from the mean for the z-score value z = -1.2857 (the value is below the mean, denoted by the minus sign). So, the cumulative probability for the latter z-score is 0.5000-0.4015=0.0985. This is the cumulative probability for P(x<41).

Well, the cumulative probability for P(x>41) is 1 - 0.0985 = 0.9015 or 90.15%. The graph below represents this cumulative probability (dark violet area).

d

step-by-step explanation:

congruent segments

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