Question

4a. A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins in the environment. Previous research had established that this trait is usually found in 1 of every 8 frogs. He collects and examines 12 frogs. If the frequency of the trait has not changed, what is the probability he finds the traits in

1. None of the frogs?

2. At least 2 frogs

4b There are three nursing positions to be filled at Lilly Hospital.  Position one is the day nursing supervisor; position two is the night nursing supervisor; and position three is the nursing coordinator position.  There are 15 candidates qualified for all three of the positions.  Use the permutations rule to determine the number of different ways the positions can be filled by these applicants.

Answer 1

(4a)

(a)

Binomial Distribution

n = 12

p = 1/8 = 0.125

q = 1 - p = 0.875

P(X=0) = qn = 0.87512 = 0.2014

So,

Answer is:

0.2014

(a)

P(X2) = 1 - [P(X=0) + P(X=1)]

P(X=0) = qn = 0.87512 = 0.2014

So,

P(X2) = 1 - [P(X=0) + P(X=1)] = 1 - (0.2014 + 0.3453) = 1 - 0.5467 = 0.4533

So,

Answer is:

0.4533

(b)

Number of permutations of 15 items taking 3 items is given by:

So,

Answer is:

2730