Question

PLEASE SHOW STEP BY STEP HOW TO DO THE PROBLEN

The mean amount of time it takes a kidney stone to pass is 15 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 18 days to pass it.

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

Answer 1

Solution :

Given that,

mean = $\mu$ = 15

standard deviation = $\sigma$ = 4

(A)X ~ N(15,4)

(B)P(x >18 ) = 1 - P(x< 18)

= 1 - P[(x -$\mu$) / $\sigma$ < (18-15) / 4]

= 1 - P(z <0.75 )

Using z table

= 1 -  0.7734

probability= 0.2266

(C)

The z dist'n uppr quartile is,

P(Z < z) = 75%

= P(Z < z) = 0.75  

= P(Z < 0.67 ) = 0.75

z = 0.67

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 0.67 * 4+15

x = 17.68

upper quartile =Q3 = 18