Question

# Old Billie and her son Hadey are arguing about how much time their fellow goats spend...

Old Billie and her son Hadey are arguing about how much time their fellow goats spend listening to music each day. Old Billie contends that the goats spend between 0 and 80 minutes each day listening to music, and she insists that no range of times is ay more likely than any other. Hadey argues that it doesn't make sense to believe that goats are just as likely to spend more time than two hours listening to music as they are to spend between 30 and fifty minutes and proposes a normal distribution instead.5) According to Hadeys conjecture, what is the probability that a random goat spends more than two hours listening to music in a day?

Solution:

Given:

Hadey argues that it doesn't make sense to believe that goats are just as likely to spend more time than two hours listening to music as they are to spend between 30 and fifty minutes and proposes a normal distribution instead.

We assumed that mean and standard deviation is same.

Mean = 40 mins

standard deviation = = 23 mins

We have to find probability that more than two hrs. 2 hrs means 120 mins.

Therefore, we have to use normal distribution to find P(X>120)

Using z-score,

P(Z > 3.4783) = 1-P(Z<3.4783)

P(Z > 3.4783) = 1−0.9997=0.0003

Hence, the probability that a random goat spends more than two hours listening to music in a day is 0.0003

Done

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