Binomial Probabilities using a Calculator

Question 1

Let X be a binomial random variable with n=10, p=.35

What is the probability notation for exactly 3 successes?

Answer 1

P(X = 3)

X represents the number of successes

Question 2

Let X be a binomial random variable with n=10, p=.35

What is the calculator input for the probability of exactly 3 sucesses

Answer 2

10 C 3 * (0.35^3) * (0.65^7)
or binompdf(10,.35,3)

This uses binompdf because it is asking exactly 3

Question 3

Let X be a binomial random variable with n=10, p=.35

What is the probability rounded to three decimal places for exactly sucesses?

Answer 3

binompdf(10,.35,3)=0.231

Question 4

Let X be a binomial random variable with n=10, p=.35

What is the probability notation for no sucesses?

Answer 4

P(X = 0)

X represents the number of successes

Question 5

Let X be a binomial random variable with n=10, p=.35

What is the calculator input for the probability of no successes?

Answer 5

10 C 0* (0.35^0) * (0.65^10)
or binompdf(10,.35,0)

This uses binompdf because it is asking exactly 0

Question 6

Let X be a binomial random variable with n=10, p=.35

What is the probability rounded to three decimal places for no successes?

Answer 6

binompdf(10,.35,0)=0.013

This uses binompdf because it is asking exactly 0

Question 7

Let X be a binomial random variable with n=10, p=.35

What is the probability notation for 10 successes?

Answer 7

P(X = 10)

X represents the number of successes

Question 8

Let X be a binomial random variable with n=10, p=.35

What is the calculator input for the probability of 10 successes?

Answer 8

₁₀ C ₁₀* (0.35^10) * (0.65^0)
or binompdf(10,.35, 10)

This uses binompdf because it is asking exactly 10

Question 9

Let X be a binomial random variable with n=10, p=.35

What is the probability rounded to three decimal places for the probability of exactly 10 successes?

Answer 9

binompdf(10,.35, 10)=0.000

calculator will display 2.759E-5 which is a very small, close to 0

Question 10

Let X be a binomial random variable with n=10, p=.35

What is the probability notation for at most 4 of successes?

Answer 10

P(X ≤ 4)
## Footnote

X represents the number of successes

Question 11

Let X be a binomial random variable with n=10, p=.35

What is the calculator input for the probability of at most 4 sucesses?

Answer 11

binomcdf(10,.35, 4)

This sums the probabilities for k from 0 to 4.

Question 12

Let X be a binomial random variable with n=10, p=.35

What is the probability rounded to three decimal places for **at most 4 **successes?

Answer 12

binomcdf(10,.35, 4)=0.829

This is the calculated probability for at most 4 successes

Question 13

Let X be a binomial random variable with n=10, p=.35

What is the probability notation for more than 6 successes?

Answer 13

P(X > 6)

Question 14

Let X be a binomial random variable with n=10, p=.35

What is the calculator input for the probability of more than 6 successes?

Answer 14

P(X > 6) = 1 - binomcdf(10,.35,6)

This calculates the complement of the probability for k from 0 to 6.

Question 15

Let X be a binomial random variable with n=10, p=.35

What is the probability rounded to three decimal places for more than 6 successes?

Answer 15

P(X > 6)=1 - binomcdf(10,.35,6)=
0.005

This is the calculated probability for more than 6 successes

Question 16

Let X be a binomial random variable with n=10, p=.35

What is the probability rounded to three decimal places for 5 or more successes?

Answer 16

P(X>= 5)

Question 17

Let X be a binomial random variable with n=10, p=.35

What is the calculator input for 5 or more successes?

Answer 17

P(X>= 5)=1-binomcdf(10,.35,4)

Question 18

Let X be a binomial random variable with n=10, p=.35

What is the probability rounded to three decimal places for 5 or more successes?

Answer 18

P(X>= 5)=1-binomcdf(10,.35,4)
=.249

This is the complimentary probability of 4 or fewer successes