A random variable X follows the uniform distribution with a lower limit of 520 a

Question

A random variable X follows the uniform distribution with a lower limit of 520 and an upper limit of 620. a. Calculate the mean and the standard deviation for the distribution. (Round intermediate calculation for Standard deviation to 4 decimal places and final answer to 2 decimal places.) b. What is the probability that X is less than 570? (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Find the following probabilities based on the standard normal variable Z. Use Table 1. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.) Find the following z values for the standard normal variable Z. Use Table 1. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Explanation / Answer

a) mean = (U + L)/2 = (620+520) / 2 = 570
standard deviation = (U - L)/12 =( 620-520) /12 =23.094

b) P(X<570) = (570 - 570)/(23.094) = 0

c) FROM THE STANDARD TABLE

WE HAVE VALUES we look into correponding values in z table

       a) p(-1.20<z<-0.88) = 0.1894 -0.1151 = 0.0743

      b) p(0.04<z<1.64)     =0.9495-0.5160 = 0.4335

     c)p(-1.56<z<0.19)      = 0.5753-0.0594= 0.5159

    d)p(z>3.9)   as it is greater than 3.4 it is high values so its probaility is 1

d)   a ) p(z<=z) =0.9186 from standard z table we have value is 1.3957 rounding to two digits =1.40

     b)p(z>z)=0.7254 =p(z<=z)=1-0.7254 =0.2746 = from standard z table we have value is -0.5758 rounding to -0.58

    c) p(-z<=Z<=z)=0.72 from standard z table we have value is 0.5828 rounding to two digits =0.58

   d)p(0<=z<=z) = 0.4813 =-0.046 rounding off two digits = - 0.05

                                                                         

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