Question

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)

Answer 1

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