A random variable, x, has a normal distribution with μ = 15.9 and σ = 2.80. Determine a value, x0, so that:
a. P(x>x0) = 0.05
x0 = ______ . (Round to one decimal place as needed.)
b. P(x≤x0) = 0.975
x0 = ______ . (Round to one decimal place as needed.)
Solution :
Using standard normal table,
a.
P(Z > z) = 0.05
1 - P(Z < z) = 0.05
P(Z < z) = 1 - 0.05
P(Z < 1.65) = 0.95
z = 1.65
Using z-score formula,
x = z * +
x = 1.65 * 2.80 + 15.9 = 20.5
b.
P(Z z) = 0.975
P(Z 1.96) = 0.975
z = 1.96
Using z-score formula,
x = z * +
x = 1.96 * 2.80 + 15.9 = 21.4
A random variable, x, has a normal distribution with μ = 15.9 and σ = 2.80....
A random variable, x, has a normal distribution with μ = 15.9 and σ = 2.80. Determine a value, x0, so that: a. P(x>x0) = 0.05 x0 = ______ . (Round to one decimal place as needed.) b. P(x≤x0) = 0.975 x0 = ______ . (Round to one decimal place as needed.)
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