A environmental scientist is studying the ecacy of sh passag

A environmental scientist is studying the ecacy of sh passages on dams. Her data collected over 2 years shows that only 1.8% of American shad (a species of sh that migrates from the sea up into fresh water to spawn) are able to pass through the Essex Dam on the Merrimack River.

a) If ten shad attempt to cross the Essex Dam, what is the probability that at least 2 make it up the dam? Round to four decimal places.

b) If 1000 shad attempt to cross the Essex Dam, what is the estimated probability that 10–20 (inclusive) make the crossing? Round to four decimal places.

c) If 200 shad attempt to cross the Essex Dam, what is the estimated probability that 4–6 (inclusive) make the crossing? Round to four decimal places.

Solution

a) probability of crossing = 0.018

probability of not crossing = 0.982

n = 10

at least 2 = 1 - P(0)+P(1)

P(0)+P(1) = 10C0(0.018)^0(0.982)^10 +10C1(0.018^1(0.982)^9 = 0.825

ANSWER = 1- 0.825 = 0.175

B)IF N = 1000

TO CALCULATE IT WE HAVE TO APPLY THE SAME FORMULA AS ABOVE BT FOR P(10)+P(11)+P(12)+.......P(20 )

P(10 ) = 1000C10(O.018)^10*(0.982)^990

SIMILARLY WE CAN FIND ALL

C) IN THIS N = 200

IN THIS WE HAVE TO CALCULATE P(4)+P(5)+P(6)

P(4) = 200C4*(0.018)^4(0.982)^196 + P(5) +P(6) = 0.230