Question

(Binomial Test) N = 10, and we obtained 6 successes and 4 failures. What is the one-tailed probability of 6 or more successes when the probability of a success is:

a. .50

b. .40

c. .30

d. .20

e. .10

For each of those probabilities, with N = 10, what is the mean and standard deviation of the distribution?

a. when p = .50

b. when p = .40

c. when p = .30

d. when p = .20

e. when p = .10

Answer 1

(1)

(a)

Binomial Distribution

N = 10

p = 0.50

So,

q = 1 - p = 0.50

From Cumulative Binomial Table, we get:
P(X6) = 0.3770

So,

Answer is:

0.3770

(b)

Binomial Distribution

N = 10

p = 0.40

So,

q = 1 - p = 0.60

From Cumulative Binomial Table, we get:
P(X6) = 0.1662

So,

Answer is:

0.1662

(c)

Binomial Distribution

N = 10

p = 0.30

So,

q = 1 - p = 0.70

From Cumulative Binomial Table, we get:
P(X6) = 0.0473

So,

Answer is:

0.0473

(d)

Binomial Distribution

N = 10

p = 0.20

So,

q = 1 - p = 0.80

From Cumulative Binomial Table, we get:
P(X6) = 0.0064

So,

Answer is:

0.0064

(e)

Binomial Distribution

N = 10

p = 0.10

So,

q = 1 - p = 0.90

From Cumulative Binomial Table, we get:
P(X6) = 0.0001

So,

Answer is:

0.0001

(2)

(a)

N = 10

p = 0.50

So,

q = 1 - p = 0.50

Mean =

Standard deviation =

(b)

N = 10

p = 0.40

So,

q = 1 - p = 0.60

Mean =

Standard deviation =

(c)

N = 10

p = 0.30

So,

q = 1 - p = 0.70

Mean =

Standard deviation =

(d)

N = 10

p = 0.20

So,

q = 1 - p = 0.80

Mean =

Standard deviation =

(e)

N = 10

p = 0.10

So,

q = 1 - p = 0.90

Mean =

Standard deviation =