Question

If the duration of kidney disease from the onset of symptoms until kidney “failure” ranges from 1 to 5 years, the average is 2.42 years with a standard deviation of 0.89 years. One administrator of a public medical center randomly selected the medical records of 41 patients with damaged kidneys. Find the probability for :

1. the average duration is less than 3.2 years.

2. the average duration exceeds 3.2 years.

3. the average duration lies within 0.8 year of the population mean

Answer 1

$P(1<Z<3.2)=P(\frac{1-2.42}{0.89}<Z<\frac{3.2-2.42}{0.89})=(-1.6<Z<0.88)$

$P=0.81057-0.0548=0.75577$

b.

$P(3.2<Z<5)=P(\frac{3.2-2.42}{0.89}<Z<\frac{5-2.42}{0.89})=(0.88<Z<2.90)$

$P=0.99813-0.81057=0.18756$

c.

$P(-0.90<Z<0.90)$

$P=0.81594-0.18406=0.63188$