Now we can move to the second question.

What's the variance and

standard deviations of the perfect Biles Move according to the statistics?

Well, we know from the theory that you learned from CAL that the formula for

the variance in a Bernoulli random variable,

is the probability multiplied by one minus the probability of the test.

In this case we will take the probability of seeing a perfect Biles Move which is

0.95 and we will multiply it by 0.05 following these rules.

Hence, this 0.0475 is the result of the variance.

Similarly we can apply the rule to calculate standard deviatioin of this

Bernoulli random variable which is just to take the square root of the variance.

If we take the square root of the variance as we can do it here we

just receive a value of 0.21794, this is a standard deviation.

Now we are asked to use the probability mass function to calculate

the probability that if Biles competes 35 times in the next years,

she conducts at least 33 perfect Biles Moves.

Okay, we have the hint here that we need to use the BINOM.DIST command in

command in Excel.

And we need to interpret this formula because this formula yields

the probability of a certain event to happen at most n times,

this means less than n times.

Hence, if we want to calculate the probability of seeing at least 33 perfect

Biles, if Simone Biles compete 35 time

we need to calculate the probability of saying at most

two failure to Simone Biles Moves out of 35 moves.

The probability of seeing a failed Simone Biles Move

is 0.05, meaning the difference between one and

the probability of seeing a perfect Biles Move which was 0.95.

And we need to here write true to state that

the formula is not cumulative meaning that we are looking for at most two failures.

Well, if we conduct this calculation, we see that the probability that we see at

least 33 perfect Biles if Simone Biles competes 35 times is of, rounded, 75%.

Now we have the last question which is use the same probability mass function to

calculate the probability that if Biles competes again, 35 times in the next year.

She conducts exactly 33 perfect Biles Move.

Well, now we can calculate something the same formula two failures

out of 35, probability of failure 0.05.

And in this case we would just right here false to say that we are looking for

exactly 33 perfect Biles.

This would get a probability of 27.4, roughly.

If we would like to apply the same formula, but using different data,

meaning using a different form we could also use this.

Look what I did here below, is instead of calculating the probability of two

failures, I would calculate the probability of 33 successes out of 35.

So we could come up here and would say probably 33 perfect Biles Moves out of 35.