唔識做呢條數... 麻煩高手請進!!!~thanks!!!

viko_rico

2009-06-04 4:47 am

An astronomer at the Mount Palomar Observatory notes that, during the Geminid Meteor shower, an average of 50 meteors appears each hour, with a variance of 9 meteors squared. The Geminid meteor shower will occur next week.

a) If the astronomer watches the shower for 4 hours, what is the probability that at least 48 meteors per hour will appear?

b) If the astronomer watches for an additional hour, will this probability rise or fall? Why?

回答 (1)

myisland8132

2009-06-04 5:05 am

✔ 最佳答案

(a) Let say the number of meteors appear each hour ~ N(50,9)
Then the number of meteors appear for 4 hours ~N(200,36)
the probability that at least 48 meteors per hour will appear
=P(N>=48*4)
=P(N>=192)
=P(Z>=(192-200)/6)
=P(Z>=-1.3333)
=0.9088
(b) Now the number of meteors appear for 5 hours ~N(250,45)
the probability that at least 48 meteors per hour will appear
=P(N>=240)
=P(Z>=(240-250)/6.7082)
=P(Z>=-1.49)
So the probability will rise. In fact, since there are 50 meteors (>48) appears each hour, when the time increase, the probability that the average meteors least 48 meteors per hour will increase

👍 0 👎 0