Solution
a).
i). P(X <150)
"=0.8413"
ii). P(X >x) =0.1
"{x-134 \\over 16}=1.28""x=1.28(16)+134"
"=154.5 \\space minutes"
b). P (Y<170)=0.14 and P(Y>200)=0.03
"{170 - \\mu \\over \\sigma} =-1.08""170- \\mu = - 1.08 \\sigma \\space........ (i)"
"P(Y>200)=1-P(Y \\le 200)=0.03"
"\\phi ({200 - \\mu \\over \\sigma}) =1-0.03=0.97"
"{200 - \\mu \\over \\sigma} =1.88""200-\\mu =1.88 \\sigma \\space...... (ii)"
Solve eq(i) and (ii) simultaneously.
Subtracting eq(i) from (ii) yields :
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