Normal Distribution From an experiment measuring the weights of 1000 random aard

Question

Normal Distribution From an experiment measuring the weights of 1000 random aardvarks, it was found that the mean aardvark weight was 80 pounds with a standard deviation of 5 pounds and that the data was normally distributed (bell shaped curve). An aardvark is picked at random: a.) What is the probability the aardvark weighs between 70 and 90 pounds? b.) What is the probability the aardvark weight is greater than 85 pounds? c.) What is the probability the aardvark weight is between 65 and 95 pounds? d.) What is probability the aardvark weight is between 80 and 85 pounds? e.) What is the probability the aardvark weight is below 80 pounds? f.) What is probability the aardvark weight is greater than 95 pounds? g.) What is the range of plausible values of the aardvark weight? h) 50% of aardvarks in the world have weight higher than 95% of aardvarks in the world have a weiaht between

Explanation / Answer

Mean is 80 and s is 5

z is given as (x-mean)/s

e) P(x<80)=P(z<(80-80)/5)=P(z<0) from normal distribution table it is 0.5

f) P(x>95)=P(z>(95-80)/5)=P(z>3) or 1-P(z<3)=1-0.9987=0.0013

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