For Problems #1 through #11, consider the following context:Felicity, a veterinary researcher specializing in feline obstetrics and neonatal care, has been collecting data on the number of kittens in first litters from female calico cats.Letxrepresents the number of kittens per litter:

x 1 2 3 4 5 6. . 7. 8. 9. 10. 11. 12

P(x). 2%. 8% 15% 25% 20% 10% ??? 5%. 4%. 3%. 2%. 1%

She accidentally omitted one entry from her probability distribution.

Complete this probability distribution table and answer the following questions:

[COMMENTS & HINTS:Express all answer involving percentages using the percent symbol.Ex:1%or99%.]

1.Record your response to item #1 here.

DetermineP(x=7)

2.Record your response to item #2 here.

P(x=7)

3.Record your response to item #3 here.

P(x<_2)

4.Record your response to item #4 here.

P(3<_x<_5)

5.What is the chance that a randomly selected female calico cat who gave birth didnothave exactlynine(9) kittens?

Answer:

6.What is the chance that a randomly selected female calico cat who gave birth hadeithertwo(2)orfour(4) kittens?

Answer:

7.What is the chance that a randomly selected female calico cat who gave birth hadneithertwo(2)norfour(4) kittens?

Answer:

8.What is the chance that a randomly selected female calico cat who gave birth hadno fewer than six(6) kittens?

Answer:

9.What is the chance that a randomly selected female calico cat who gave birth hadat most six(6) kittens?

Answer:

10.What is the chance that a randomly selected female calico cat who gave birth hadmore than seven(7)but less than twelve(12)kittens?

Answer:

11.What is themodalnumber of kittens born in a female calico cat's first litter?

Answer:

12.Themediannumber of kittens born in a female calico cat's first litter is exactly4.5 kittens, or equally split between4 and 5 kittens.

True

False

13.On average, how many kittens are in a female calico cat's first litter?[COMMENTS & HINTS:What is the expectation or expected value for this random variable?Express the answer rounded to the nearest whole number.Enter only as a counting number: report approximately8.49days only as8, or approximately9.50days only as10.]

Answer:

14.What is the shape of this probability distribution, based upon the percentages?[COMMENTS & HINTS:Select the most appropriate response.]

1. Bimodal
2. J-shaped
3. Rectangular or Uniform
4. Skewed Left or Negatively Skewed
5. Skewed Right or Positively Skewed
6. Symmetric or Triangular

a.response (a):Bimodal

b.response (b):J-shaped

c.response (c):Rectangular or Uniform

d.response (d):Skewed Left or Negatively Skewed

e.response (e):Skewed Right or Positively Skewed

f.response (f):Symmetric or Triangular

15.Felix, a fellow feline obstetrics researcher, reviews her Felicity's probability distribution.He wonders why the random variable ends with 12 kittens per first litter, since he claims he once witnessed one female calico cat give birth to 13 kittens in her first litter.What's the most reasonable or plausible explanation?

a.Response (a):Litters larger than 12 kittens never ever actually happen, despite his claim.

b.Response (b):Discrete random variables can never can take on more than one-dozen values.

c.Response (c):The likelihood that a female calico cat has more than 12 kittens in her first litter is absolutely and exactly zero percent.

d.Response (d):The likelihood that a female calico cat has more than 12 kittens in her first litter is statistically insignificant.

e.Response (e):The chance that a female calico cat has more than 12 kittens in her first litter is so unlikely that the individual and cumulative percentages rounds to zero, and is consistent with the apparent declining probabilities as litter sizes increase in the probability distribution table.

16.According to cytogenetics, the likelihood of a calico cat being male is very high.

True

False