PLEASE SHOW ALL WORK! Weights of female cats of certain breed are normally distr

Question

PLEASE SHOW ALL WORK!

Weights of female cats of certain breed are normally distributed with mean 4.1 kg and standard deviation 0.6 kg.

a. What proportion of female cats have weights between 3.7 and 4.4 kg?
b. A certain female cat has a weight that is 0.5 standard deviations above the mean. What porportion of female cats are heavier than this one?
c. How heavy is a female cat whose weight is on the 80th percentile?
d. A female cat is chosen at random. What is the probability that she weighs more than 4.5 kg?
e. six female cats are chosen at random. What is the probability that exactly one of them weighs more then 4.5 kg?

Explanation / Answer

a) z scores are (4.4-4.1)/0.6= 0.5 and (3.7-4.1)/0.6 = -0.67 Consulting a normal table we have .6915-.2514= .4401 b) We know from a) that the probability of less than 0.5 is .6915. So the probability of greater is 1-.6915= .3085. c) Consulting a normal curve table the 80th percentile has a z score of 0.84. So 0.84= (x-4.1)/0.6 Solving for x we get 4.604. d) 4.5 has a z score of (4.5-4.1)/0.6= 0.67. Consulting a normal table we get 0.7486 is less, so 1-0.7486= 0.2514. e) Using the binomial theorem with p= .2514 we get 6!/5!*1! (.2514)^1* (.7486)^5= 0.355

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.