The time required to assemble an electronic component is normally distributed wi

Question

The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 32 minutes and 12 minutes, respectively. Use Table 1.

Find the probability that a randomly picked assembly takes between 19 and 37 minutes. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

It is unusual for the assembly time to be above 51 minutes or below 19 minutes. What proportion of assembly times fall in these unusual categories? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Find the probability that a randomly picked assembly takes between 19 and 37 minutes. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Explanation / Answer

Mean is 32 and s is 12. z is (x-mean)/s

a) P(19<x<37)= P((19-32)/12<z<(37-32)/12) =P(-1.08<z<0.42) =P(z<0.42)-P(z<-1.08) . from normal distribution table we get 0.6628-(1-0.8599)=0.5227

b) To find P(19<x<51) =P((19-32)/12<z<(51-32)/12) =P(-1.08<z<1.58)=P(z<1.58)-P(z<-1.08)=0.9429-(1-0.8599)= 0.0582

thus answer is 1-0.0582=0.9418

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