Question

A
random variable follows a binomial distribution with a probability
of success equal to 0.52. For a sample size of n=7, find the values
below.

a. the probability of exactly 3 successes

b. the probability of 4 or more successes

c. the probability of exactly 7 successes

d. the expected value of the random variable

Answer #1

Please note ^{n}C_{x} = n! / [(n-x)!*x!]

Binomial Probability = ^{n}C_{x} *
(p)^{x} * (q)^{n-x}, where n = number of trials and
x is the number of successes.

Here n = 7, p =0.52, q = 1 – p = 0.48

_____________________________

(a) P(X = 3) = ^{7}C_{3} * (0.52)^{3} *
(0.48)^{7-3 = 4} = **0.2612**.

____________________________

(b) P(4 or More) = (X 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

P(X = 4) = ^{7}C_{4} * (0.52)^{4} *
(0.48)^{7-4 = 3} = .0.2830

P(X = 5) = ^{7}C_{5} * (0.52)^{5} *
(0.48)^{7-5 = 2} = .0.1840

P(X = 6) = ^{7}C_{6} * (0.52)^{6} *
(0.48)^{7-6 = 1} = .0.0664

P(X = 7) = ^{7}C_{7} * (0.52)^{7} *
(0.48)^{7-7 = 0} = .0.0103

Therefore P(X > 4) = 0.2830 + 0.1840 + 0.0664 + 0.0103 =
**0.5437**

______________________________

(c) P(X = 7) = ^{7}C_{7} * (0.52)^{7} *
(0.48)^{7-7 = 0} = .**0.0103**

________________________________

(d) Expected value = n * p = 7 * 0.52 = **3.64**

**_______________________________**

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b. the probability of 7 or more successes
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d. the expected value of the random variable

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a. What
is the expected number of successes in 90 trials?
b. What
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c. Use
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d. Use
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1. There there are two mutually exclusive outcomes
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[ Select ]
["FALSE",
"TRUE"]
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e.
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