In hawaii, january is a favorite month for surfing since 60% of the days have a surf of at least 6 feet.† you work day shifts in a honolulu hospital emergency room. at the beginning of each month you select your days off, and you pick 6 days at random in january to go surfing. let r be the number of days the surf is at least 6 feet. what is the probability of getting 4 or more days when the surf is at least 6 feet? (round your answer to three decimal places.)

The probability of getting 4 or more days when the surf is at least 6 feet is 0.544

Step-by-step explanation:

We can modelate this exercise as a binomial random variable.

The probability function of a binomial random variable is :

Where is the probability of the variable X to assume the value r

nCr is the combinatorial number define as

n is the number of binomial experiments that we make. In our exercise, n is the number of random days we pick of January.

And finally p is the success probability.

In our exercise, we define X : ''The number of days when the surf is at least 6 feet''.

And we are looking for P(X≥4).

P(X≥4) = P(X = 4) + P(X = 5) + P(X = 6)

Finally

P(X≥4)=

P(X≥4) = 0.544

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)