1. Weights of female cats of a certain breed are normally distributed with mean

Question

1. Weights of female cats of a 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 4.4kg? (6 points) b. A certain female cat has a weight that is 0.5 standard deviations above the mean What proportion of female cats are heavier than this one? (6 points) c. How heavy is a female cat whose weight is on the 80th percentile? (6 points) d. A female cat is chosen at random. What is the probability that she weights more than 4.5kg? (6 points,) e. Six female cats are chosen at random. What is the probability that exactly two of them weight more 4.5kg? (6 points)

Explanation / Answer

Ans:

z=(x-4.1)/0.6

a)

z(3.7)=(3.7-4.1)/0.6=-0.67

z(4.4)=(4.4-4.1)/0.6=0.5

P(-0.67<=z<=0.5)=P(z<=-0.67)-P(z<=0.5)=0.6915-0.2514=0.4400

b)P(z>0.5)=1-0.6915=0.3085

c)P(Z<=z)=0.8

z=0.8416

x=4.1+0.8416*0.6=4.60

d)z=(4.5-4.1)/0.6=0.67

P(z>0.67)=1-0.7486=0.2514

e)use binomial distribution:

P(y=2)=6C2*0.25142*(1-0.2514)4

=0.2977

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