Question

4. Determine the x value if X is a normal random variable with mean 40 and standard deviation 6.
a) ?(? > ?) = 0.5
b) ?(? > ?) = 0.28
c) ?(? < ?) = 0.82

Answer 1

a)

The following information has been provided: μ=40, σ=6 We need to find a score x so that the corresponding cumulative normal probability is equal to 0.5. Mathematically, x is such that: P(X>x) = 0.5 or Pr(X≤x)=0.5 The corresponding z score so that the cumulative standard normal probability distribution is 0.5 is zc​=0 This value of zc​=0 can be found either with Excel, or with a normal distribution table. Hence, the X score associated with the 0.5 cumulative probability is

b)

The following information has been provided: μ=40, σ=6 We need to find a score x so that the corresponding cumulative normal probability is equal to 0.72. Mathematically, x is such that: P(X>x) =0.28 or Pr(X≤x)=0.72 The corresponding z score so that the cumulative standard normal probability distribution is 0.72 is zc​=0.5828 This value of zc​=0.5828 can be found either with Excel, or with a normal distribution table. Hence, the X score associated with the 0.72 cumulative probability is

c)

The following information has been provided: μ=40, σ=6 We need to find a score x so that the corresponding cumulative normal probability is equal to 0.82. Mathematically, x is such that: Pr(X≤x)=0.82 The corresponding z score so that the cumulative standard normal probability distribution is 0.82 is zc​=0.9154 This value of zc​=0.9154 can be found either with Excel, or with a normal distribution table. Hence, the X score associated with the 0.82 cumulative probability is

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