Question

The mean amount of time it takes a kidney stone to pass is 12 days and the standard deviation is 4 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N

b. Find the probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it.


c. Find the minimum number for the upper quarter of the time to pass a kidney stone.
days.

Answer 1

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

$\rm P ( \dfrac{x - \mu }{\sigma} < \dfrac{x_0 -13}{6}) = 0.75$

$\rm \phi (\dfrac { x_o - 12}{4}) = 0.75$

Using the excel function the z score for the area 0.75 is

z - score = 0.6745

$\rm \dfrac {x_o - 12}{4} = 0.6745$

x₀  = 0.6 * 4 + 12

x₀ = 14.4

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