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 11 days to pass it.
c. Find the minimum number for the upper quarter of the time to pass a kidney stone. (Hint: the number at which 25% takes longer than) days.
Answer:
Given:
The population mean $(μ)=13$
The population standard deviation $(\sigma)=5$
Solution:
(A) The distribution of x : X~N (13,5)
(B) The probability that a randomly selected person with a kidney stone will take longer than 11 days to pass it:
$P(x > 11) = P\left(\frac{x – \mu}{\sigma} > \frac{11 – 13}{5}\right) = P(z > -0.4) = 0.6554$
C) The minimum number for the upper quarter of the time to pass a kidney stone:
→ The z-score for right probability 0.25 = 0.6725
Here we use a z-score formula to find out the x value:
$$z = \frac{x – \mu}{\sigma} \quad $$ $$ \therefore 0.6745 = \frac{x – 13}{5} \quad $$ $$\therefore x = 16 $$
