Compute the following binomial probabilities using the table of
Cumulative Binomial Probabilities. Give your answer to
3 places past the decimal.
c) Binomial pmf value: b(10; 15, 0.3)
d) Binomial pmf value: b(11; 20, 0.4)
e) P(2 ≤ X ≤ 7) when X ~ Bin(15, 0.2)
f) P(X ≥ 9) when X ~ Bin(15, 0.2)
g) P(6 < X ≤ 9) when X ~ Bin(15, 0.2)
1. Find all solutions to the following linear congruences using
Fermat’s Little Theorem or Euler’s Theorem to help you. Show all
your steps.
(a) 3462x ≡ 6 173 (mod 59)
(b) 27145x ≡ 1 (mod 42)
Use Stokes' Theorem to find the circulation of F⃗ =2yi⃗ +2zj⃗
+4xk⃗ around the triangle obtained by tracing out the
path (3,0,0) to (3,0,4), to (3,4,4) back to (3,0,0).
Circulation = ∫CF⃗ ⋅dr⃗ =
Second time I've asked this question because chegg cant solve
this problem correct. 24sqrt(2) is the wrong answer
Use Stoke's Theorem to find the circulation of F⃗ =7yi⃗ +3zj⃗
+2xk⃗ around the triangle obtained by tracing out the path (5,0,0)
to (5,0,3) to (5,5,3) back to (5,0,0)
Small triangle. Answer the following.
a. State a definition for small triangle that would eliminate a
counterexample to ASA.
b. Explain why using this definition eliminates the possibility
of a counterexample to ASA.
Suppose 16 coins are tossed. Find the probability of getting the
following result using the binomial probability formula and the
normal curve approximation.
Exactly 6 heads.
Binomial probability =
(Round to 4 decimal places.)
Normal curve approximation almost =
(Round to 4 decimal places.)
Find to 4 decimal places the following binomial probabilities
using the normal approximation.
a. n = 140, p = 0.42, P(x = 64)
P(x = 64) =
b. n = 100, p = 0.58, P(51 ≤ x ≤ 60)
P(51 ≤ x ≤ 60) =
c. n = 90, p = 0.42, P(x ≥ 41)
P(x ≥ 41) =
d. n = 102, p = 0.74, P(x ≤ 75)
P(x ≤ 75) =
Find to 4 decimal places the following binomial probabilities
using the normal approximation.
a. n = 130, p = 0.42,
P(x = 77)
P(x = 77) =
b. n = 100, p = 0.57,
P(52 ≤ x ≤ 61)
P(52 ≤ x ≤ 61) =
c. n = 90, p = 0.41,
P(x ≥ 38)
P(x ≥ 38) =
d. n = 103, p = 0.75,
P(x ≤ 75)
P(x ≤ 75) =
Using Fermat't Little Theorem for primality test. Answer the
following. Show work for credit.
(a) Test whether each of the following numbers is primes: 101,
341, and 1105. Try at least two bases if needed, and state if the
number is pseudoprime to any base you try. You may use a claculator
to compute large powers. (MS Excel can be used)
(b) Find a composit number that is pseudoprime to base 3 and 7
but not pseudoprime to base 2...