Let "X" be a random variable which denotes the call duration in minutes. Our random variable "X" is normal
"X\\sim N(\\mu,\\sigma^2)". Then
"Z={X-\\mu \\over \\sigma}\\sim N(0,1)" Given that "\\mu=6.3 \\ minutes, \\sigma=2.2 \\ minutes."
a.
"P(5<X<10)=P\\bigg({5-6.3 \\over 2.2}<Z<{10-6.3 \\over 2.2}\\bigg)=""=P\\bigg(Z<{3.7 \\over 2.2}\\bigg)-P\\bigg(Z<{-1.3 \\over 2.2}\\bigg)\\approx""\\approx0.953698-0.277291\\approx0.6764"
b.
"P(X>7)=P\\bigg(Z>{7-6.3 \\over 2.2}\\bigg)=1-P\\bigg(Z<{0.7\\over 2.2}\\bigg)\\approx""1-0.624826\\approx0.3752"
c.
"P(X<4)=P\\bigg(Z<{4-6.3\\over 2.2}\\bigg)=P\\bigg(Z<{-2.3\\over 2.2}\\bigg)\\approx""\\approx0.1479"
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