Please I want someone to redo it clearly \"step by step\" If X is Normally distr

Question

Please I want someone to redo it clearly "step by step"

If X is Normally distributed random variable with a mean of 3 and a standard deviation of 6, find the value of x for which the following is true: The mean time required for a maintenance person to purge the heat exchanger on the Sonic Washer is 12.5 minutes. A revised purging procedure has been proposed which is claimed to reduce the purging time. After being introduced to the new procedure and gaining familiarity with it through practice, the purge times using the revised procedure were recorded for 10 randomly selected purging sessions. The sample average and sample standard deviation for these 10 purge times were 11.9 minutes and 1.2 minutes, respectively. The supervisor would like to know if there has been a significant improvement in the average purging time with the revised procedure at a 5% significance level. Which are the appropriate hypotheses to test if the supervisor wishes to find strong evidence that the mean purging time has been reduced? (i) Ho: mu = 12.5 H_1: mu notequalto 12.5 (ii) Ho: mu lessthanorequalto 12.5 H_1: mu > 12.5 (iii) Ho: mu greaterthanorequalto 12.5 H_1: mu 11.9

Explanation / Answer

4)(3<X<x) =0.346

P(X<x) -P(Z<(3-3)/6)=0.346

P(X<x)-P(Z<0)=0.346

P(X<x) -0.5=0.346

P(X<x) =0.846

for 0.846 p[ercentile z=1.0194

hence x=3+1.0194*6=9.1164

5)option (iii) ius correct for hypothesis

critical value at 0.05 level and 9 degree of freedom t=-1.833

hence rejection region t<-1.833

std error =std deviation/(n)1/2 =0.3795

test stat t=(X-mean)/std error =(11.9-12.5)/0.3795=-1.58

as test stat is greater then critical value we can not reject null hypothesis that maintenance time has improved

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