Question

If the average survival of a red cell in the human body is 120 days with a standard deviation of 8 days, what is the probability for each of the following events? Assume a normal distribution,

	a.	A red cell surviving more than 134 days?
	b.	A red cell that survives less than 110 days?
	c.	A red cell surviving between 108 and 122 days?

Answer 1

Solution :

Given that ,

a.

P(x > 134) = 1 - P(x < 134)

= 1 - P[(x - ) / < (134 - 120) / 8)

= 1 - P(z < 1.75)

= 1 - 0.9599

= 0.0401

Probability = 0.0401

b.

P(x < 110) = P[(x - ) / < (110 - 120) / 8]

= P(z < -1.25)

= 0.1056

Probability = 0.1056

c.

P(108 < x < 122) = P[(108 - 120)/ 8) < (x - ) /  < (122 - 120) / 8) ]

= P(-1.5 < z < 0.25)

= P(z < 0.25) - P(z < -1.5)

= 0.5987 - 0.0668

= 0.5319

Probability = 0.5319