ary Question 1: [12 marks: a) 2, b) 2, c) 2, d) 3, e) 3] The mean weight of adul

Question

ary Question 1: [12 marks: a) 2, b) 2, c) 2, d) 3, e) 3] The mean weight of adult Siberian tigers is 150 pounds, with a standard deviation of 8 pounds The distribution of Siberian tiger weights is approximately normal. Please use this information to answer the following questions: a) True or False: If one tiger is randomly selected, there is a good chance that the tiger weighs precisely 150 pounds. b) If one tiger is randomly selected, what is the probability that it weighs more than 155 pounds? c) If one tiger is randomly selected, what is the probability that it weighs at most 146 pounds? d) If one tiger is randomly selected, what is the probability that it weighs between 140 and 155? e) If you take a sample of 15 tigers, what is the probability that the mean for that sample is more than 155 pounds?

Explanation / Answer

Ans:

a)As,weight is normally distributed and mean=150,so,there is good chance that tiger weighs approximately 150.(true)

b)

z=(155-150)/8=0.625

P(x>155)=P(z>0.625)=0.2660

c)

z=(146-150)/8=-0.5

P(x<=146)=P(z<=-0.5)=0.3085

d)

z(140)=(140-150)/8=-1.25

P(140<x<=155)=P(-1.25<z<0.625)

=P(z<0.625)-P(z<-1.25)

=0.7340-0.1056=0.6284

e)standard error of mean=8/sqrt(15)

z=(155-150)*sqrt(15)/8=2.42

P(z>2.42)=0.0078

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