Question

Researchers wanted to see which species of lizard (A, B, or C) is most likely to survive a bacterial infection. So they infected a total of 38 lizards and recorded how many survived after 48 hours. Of the 15 species B lizards, 40% survived. For those that were species C, one more survived than died. And of the 24 lizards that died, one-third of them were species A.

a. Create a contingency table to display this data.

b. What proportion of these lizards in this study were either species A or B?

c. What is the probability that a species C lizard in this study did not survive?

Answer 1

A contingency table was created using given data on lizard species survival rates following a bacterial infection. The proportion of lizards that were either species A or B was calculated to be 15/38, and the probability that a species C lizard did not survive is 11/23.

Step-by-step explanation:

Contingency Table Creation and Probability Calculation

To answer the student's question, let's start by constructing a contingency table using the information provided about the lizard species and survival rates after bacterial infection. Let's also solve for the proportion of lizards that are either species A or B, and the probability that a species C lizard did not survive.

Part A: Contingency Table

Let's start with species B. We know there were 15 of species B, and 40% survived, which equals 6 surviving and 9 not surviving (since 15 * 0.4 = 6).

For species C, more survived than died, so if 'x' is the number of those who died, 'x+1' is the number who survived. Given that 24 lizards died, we can express this as x + (x+1) = 24, yielding x = 11.5. Since we cannot have half a lizard, we must assume that the number of deaths for species C was 11, leading to 12 surviving (since one more survived than died).

For species A, we know one-third of the 24 lizards that died were of species A, so 8 of species A died. The total of species A can be deduced by subtracting the sum of species B and C lizards from the 38 total lizards, which is 38 - (15+23) = 0. So there were no surviving lizards of species A.

The contingency table would look like this:

Species
Survived
Did Not Survive


A
0
8


B
6
9


C
12
11

Part B: Proportion of Species A or B

There are no lizards of species A that survived, and there were 15 lizards of species B. So the total lizards that are either species A or B is 15 (all of which are species B). The proportion of these lizards in the study is 15/38.

Part C: Probability for Species C

For species C, 12 survived and 11 did not. Therefore, the probability that a species C lizard did not survive is 11/(12+11), which is 11/23.

Answer 2

A) attached below

B) 0.61

C) 0.47

Step-by-step explanation:

Given data:

Total number of lizards infected = 38

Of the 15 species B lizards 40% survived

For specie C one more survived than died

Out of the 24 lizards that died 1/3 were species A

A) contingency table

attached below

B) Determine the proportion of these lizards in this study that were either specie A or Specie B

P ( A or B ) = ( 8 + 15 ) / 38 = 0.605 ≈ 0.61

C) determine the probability that specie C lizard did not study

P ( not surviving | C ) = 7 / 15 = 0.466 ≈ 0.47