Question

5. Suppose a random variable, x, arises from a binomial experiment. If n = 23, and p= 0.22, find the following probabilities using technology. show work

1. P (x = 21)
2. P (x = 6)
3. P (x = 12)
4. P (x<=14)
5. P (x >=17)

6. P (x <= 9)

Answer 1

Given,

n= 23 , p=0.22

Excel function :

BINOM.DIST function

Returns the individual term binomial distribution probability. Use BINOM.DIST in problems with a fixed number of tests or trials, when the outcomes of any trial are only success or failure, when trials are independent, and when the probability of success is constant throughout the experiment. For example, BINOM.DIST can calculate the probability that two of the next three babies born are male.

Syntax

BINOM.DIST(number_s,trials,probability_s,cumulative)

The BINOM.DIST function syntax has the following arguments:

• Number_s     Required. The number of successes in trials.

• Trials     Required. The number of independent trials.

• Probability_s     Required. The probability of success on each trial.

• Cumulative     Required. A logical value that determines the form of the function. If cumulative is TRUE, then BINOM.DIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are number_s successes.

1. P (x = 21) = BINOM.DIST(21,23,0.22,FALSE) = 0.0000
2. P (x = 6) = BINOM.DIST(6,23,0.22,FALSE) = 0.1676
3. P (x = 12) = BINOM.DIST(12,23,0.22,FALSE) = 0.0011
4. P (x<=14) = BINOM.DIST(14,23,0.22,TRUE) = 1.0000
5. P (x >=17) = 1-P(x<=16) = 1-BINOM.DIST(16,23,0.22,TRUE) =1 -1.0000=0.0000
6. P (x <= 9) = BINOM.DIST(9,23,0.22,TRUE) = 0.9825