Answer to Question #124237 in Statistics and Probability for Evelyn Teye

Question

If u=3 and standard deviation =0.5, find P(x>4). If it's necessary to reduce this probability to 0.01,to what value must be changed;keeping standard deviation constant.

Answer 1

since we know both the mean and standard deviation we use the formula, z = (x-µ)/std to calculate the test statistic then use z normal tables to calculate the probability.

z = (x-µ)/std, z= (4-3)/0.5 , z= 2 thus the probability p(x>4) is the probability whose z value = 2

thus p(x>4) = 0.0227

If we want to reduce the probability to 0.01 we increase the margin of error by using a value greater than 4. The critical region for o.o1 is 2.58 so we use z value as 2.58 and calculate the margin of error. z = (x-µ)/std, 2.58 = (x--µ, )/0.5 thus , (x-u) = 1.29 and µ = 3

so x-3 = 1.29,x=4.29 thus we should use x= 4.29 instead of 4.