and percents to ens decimal plaREL2S3 If a problem about ions round the probabil

Question

and percents to ens decimal plaREL2S3 If a problem about ions round the probabilities to Instruct measurements units, write the answer wilhunits.Lsusbus24ozh. When using calculator program, write down what program you use and what values you enter: normalcdf(LU, H. a. invNorm(area.HJa) Sketch bell shape and shade the necessary area, if needed lfthere is not enough space to show work, attach your work on separate paper. Write the answers on the right for each problem. Using the following uniform distribution, find the prohabilio Pal answer the question (m.2). 1) What is the probability that the random variable x has a value greater than 4? 2) What is the probability that the random variable x has a value between 2.5 and 4.7? 2) If z is a standard normal variable, find the following 3-7). 3) The probability that z lies between 0 and 2.75 4) The probability that z lies between -2.1 and 0 5) The probability that z is less than 1.53 6) The probability that z lies between -0.5 and 0.5 7) The probability that zis greater than -1.88 The scores on a certain Statistic test in Mrs. Lindgren's class are distributed normally, with the mean u 76.4 and the standard deviation o 1.3 8-10) 8) Find Pso, the 90 percentile 9) Find Q3, the first quartile 10) If the students with the score in the lowest 5% of the class are asked to re-take the test, find the score that separates the lowest 5% from the rest. 10) Assume that the values of x are normally distributed (a10-14) The mean 60.0, the standard deviation 4.0. Find P (x

Explanation / Answer

Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
Q3.
P(X < 0) = (0-0)/1
= 0/1 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(X < 2.75) = (2.75-0)/1
= 2.75/1 = 2.75
= P ( Z <2.75) From Standard Normal Table
= 0.99702
Q4.
P(0 < X < 2.75) = 0.99702-0.5 = 0.497                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -2.1) = (-2.1-0)/1
= -2.1/1 = -2.1
= P ( Z <-2.1) From Standard Normal Table
= 0.01786
P(X < 0) = (0-0)/1
= 0/1 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(-2.1 < X < 0) = 0.5-0.01786 = 0.4821                  
Q5.
P(X < 1.53) = (1.53-0)/1
= 1.53/1= 1.53
= P ( Z <1.53) From Standard Normal Table
= 0.937                  
Q6.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -0.5) = (-0.5-0)/1
= -0.5/1 = -0.5
= P ( Z <-0.5) From Standard Normal Table
= 0.30854
P(X < 0.5) = (0.5-0)/1
= 0.5/1 = 0.5
= P ( Z <0.5) From Standard Normal Table
= 0.69146
P(-0.5 < X < 0.5) = 0.69146-0.30854 = 0.3829                  
Q7.
P(X > -1.88) = (-1.88-0)/1
= -1.88/1 = -1.88
= P ( Z >-1.88) From Standard Normal Table
= 0.9699                  

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