In: Math
You have 120 mice lacking insulin receptors in their brain tissue. On average 15.2% of these types of mice will die within a month. What is the probability at least 100 mice live until next month? (use binomial approximation of normal)
Solution:
Given,
n = 120
On average 15.2% of these types of mice will die within a month.
On average 84.8% of these types of mice will live until the next month.
Let X denotes No. of mice out of 120 that will live until the next month.
p = 84.8% = 0.848
X follows Binomial(120 , 0.848)
According to the Normal approximation to the binomial , X follows Normal distribution with
Mean = = n * p = 120 * 0.848 = 101.76
Standard deviation = =n*p*(1-p) = 120*0.848*0.15.2 = 15.46752 = 3.93287681
Find P(at least 100 mice live until next month)
= P(X 100)
= P(X > 99.5) .... Continuity correction
= P[(X - )/ > (99.5 - )/]
= P[Z > (99.5 - 101.76)/ 3.93287681]
= P[Z > -0.5746]
= 1 - P[Z < -0.5746]
= 1 - 0.2828 ( use z table)
= 0.7172