Question

= Question 5 of 7 (1 point) Question Attempt: 1 of Unlimited 1 2 3 6 7 Let Z be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places ? P(Z 5 -1.08) = 0 r(z > 1.79) - 0 P(-0.63 < Z < 1,86) = 0

Answer 1

Solution

1)

The following information has been provided: p=0, =1 We need to compute Pr(X<-1.08). The corresponding z-value needed to be computed: X - μ 1.08 - 0 Z -1.08 0 1 Therefore, Pr(X < -1.08) = Pr (Z< 1.08 - 0 1 -) = = Pr(Z < -1.08) = 0.140 The following is obtained graphically: Standard Normal Distribution: Pr(Z<-1.08)=0.1401 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

b)

The following information has been provided: H = 0, o=1 We need to compute Pr(X > 1.79). The corresponding z-value needed to be computed is: X - μ 1.79-0 Z= 1.79 0 1 Therefore, we get that Pr(X 2 1.79) = Pr(22 1.79 - 0 1 19-9) = Pr(Z > 1.79) = 1-0.9633 = 0.0367 The following is obtained graphically: Standard Normal Distribution: Pr(2>1.79)=0.0367 0.40 0.35 0.30 0.25 0.20 0.15 - 0.10 0.05 0.00 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

c)

The following information has been provided: A = 0, 0 =1 We need to compute Pr(-0.63 < X < 1.86). The corresponding z-values needed to be computed are: X1 - u -0.63 - 0 21 = -0.63 0 1 μ 1.86 - 0 22 = = 1.86 1 Therefore, we get: Pr(-0.63 < X < 1.86) = Pr -0.63 - 0 1.86 - 0 << 1 1 = Pr(-0.63 <Z < 1.86) = Pr(Z < 1.86) - Pr(Z < -0.63) = 0.9686 - 0.2643 = 0.704

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