Question

A plumber knows that the probability he will get called on any given weekday (Monday through Friday) is 0.95. What is the probability that he only gets called on one week day? A plumber knows that the probability he will get called on any given weekday (Monday through Friday) is 0.95. What is the probability that he only gets called three week days or more? X is a random variable that is normally distributed with mean 100 and standard deviation 20. That is, X~N(100, 20). What is P(X = 100)?

A plumber knows that the probability he will get called on any given weekday (Monday through Friday) is 0.95. What is the probability that he only gets called on one week day?

A plumber knows that the probability he will get called on any given weekday (Monday through Friday) is 0.95. What is the probability that he only gets called three week days or more?

Answer 1

The probability density function is given by
f(x) = 1
σ π2
μ
σ μ σ
exp ( ) , ;
, −
⎡ −
⎣
⎢
⎢
⎤
⎦
⎥
⎥
−∞ < < ∞
−∞ < < ∞ >
x x 2
2 2 0
where μ and σ are parameters. These turn out to be the mean and standard deviation,
respectively, of the distribution. As a shorthand notation, we write X ~ N(μ,σ
2
).
The curve never actually reaches the horizontal axis buts gets close to it beyond about 3
standard deviations each side of the mean.
For any Normally distributed variable:
68.3% of all values will lie between μ −σ and μ + σ (i.e. μ ± σ )
95.45% of all values will lie within μ ± 2 σ
99.73% of all values will lie within μ ± 3 σ