1.)
We are dealing with the standard normal distribution, with parameters:
μ=0, σ=1
We need to find a z-score z so that the corresponding cumulative normal probability is equal to 0.9718.
Mathematically, z is such that:
The corresponding z score so that the cumulative standard normal probability distribution is 0.9718 is
z_c = 1.9079
This value of z_c = 1.9079 can be found with a normal distribution table.
hence z = 1.9079
2)
The following information has been provided:
μ=100, σ=15
We need to compute Pr (75≤X≤115).
The corresponding z-values needed to be computed are:
Therefore, we get:
3)
We know that X is normally distributed, with parameters:
μ=100, σ=15
Pr[X >= x] = 0.9 which is same as Pr[ X < x ] = 0.1
We need to find a score x so that the corresponding cumulative normal probability is equal to 0.1.
Mathematically, x is such that:
The corresponding z score so that the cumulative standard normal probability distribution is 0.1 is
This value of z_c = 1.2816 with a normal distribution table.
Hence, the X score associated with the 0.1 cumulative probability is
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