Question

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 any more likely than any other. Hadey argues that it doesn’t make sense to believe that goats are just as likely to spend more than two hours listening to music as they are to spend between 30 and fifty minutes and proposes a normal distribution instead. Assume that Old Billie and Hadey's distribution have the same mean and standard deviation.

1. According to Hadey’s conjecture, what is the probability that a random goat spends more than two hours listening to music in a Day?

2. According to Old Billie’s conjecture, what would be the 95th percentile of the amount of time the goats spend listening to music in a day?

3. According to Hadey’s conjecture, what would be the 95th percentile of the amount of time the goats spend listening to music in a day?

Answer 1

We know that for normal distribution

mean lies at the centre(due to symmetry of the graph:

hence, mean=

here Mean(hadey)===40

Mean(old billie)===40

also the maximum and minimum values for normal distribution is obtained by=

for Hadey:

40+3=50

=

=3.33

for billie:

40+3=80

=

=13.33

	Mean	Standard deviation
Hadey	40	3.33
Billie	40	13.33

(A)HADEY:

X=time spent by goats

P(X>2)=1-P(X2)

=1-P(Z)

=1-P(Z-11.41)

P(X>2)=1

(B)BILLIE:

P(X<K)=0.95

P(Z<)=0.95

=1.65

K=1.65*13.33+40

K=61.99=62 hours

(C)HADEY

P(X<K)=0.95

P(Z<)=0.95

=1.65

K=1.65*3.33+40

K=45.49=45.5 hours

please rate my answer and comment for doubts.