Respuesta :
The probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it is 0.15866 , the minimum number for the upper quarter of the time to pass a kidney stone days is 14.4 .
What is Probability ?
Probability is the measure of likeliness of an event to happen
Let X denote the time to pass the kidney stone.
The random variable X follows normal Distribution
mean = 12 days days
standard deviation = 4 days
The distribution of X is X - N ( 12 , 4)
The probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it is
P ( X > 16) = 1 - P( X ≤ 16)
= 1 - P( Z ≤ (16-12)/4)
= 1 - P ( Z ≤ 1 )
= 1 - 0.84134
= 0.15866
P( X < x₀) = 0.75
[tex]\rm P ( \dfrac{x - \mu }{\sigma} < \dfrac{x_0 -13}{6}) = 0.75[/tex]
[tex]\rm \phi (\dfrac { x_o - 12}{4}) = 0.75[/tex]
Using the excel function the z score for the area 0.75 is
z - score = 0.6745
[tex]\rm \dfrac {x_o - 12}{4} = 0.6745[/tex]
x₀ = 0.6 * 4 + 12
x₀ = 14.4
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