Please explain how to solve these problems, thank you!!!! And please answer both

Question

Please explain how to solve these problems, thank you!!!! And please answer both questions and sub parts.

Problem 2 From many years of observation, a biologist knows that the probability that any given Arctic tern wil- survive the migration from its summer nesting area to its winter feeding grounds is only 0.65. A random samples 500 Arctic terns were banded at their summer nesting area. (1) (13 points) What is the approximate probability that less than 3 10of the banded Arctic terns will survive the migration? P:O-es,sRS500. 310 - 13 22 513

Explanation / Answer

a) p = 0.65
sd(p^) = sqrt(pq/n) = sqrt(0.65*0.35/500) = 0.021330
P( X < 310)
= P(p^ < 310/500)
= P(p^ < 0.62)
=P(Z <(0.62 - 0.65)/0.021330)
= P(Z < -1.4064697)
= 0.079799

b) P(310 < X< 340)
= P(0.62 < p^ < 0.68)
= P ( 1.41<Z<1.41 )=0.8414

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