Suppose thatxis a binomial random variable withn= 5,p= 0.78, andq= .22.

(b)For each value of x, calculate p(x).(Round final answers to 4 decimal places.)

p(0) =,p(1) =,p(2) =,p(3) =

p(4) =,p(5) =

(c)FindP(x= 3).(Round final answer to 4 decimal places.)

P(x=3)

(d)FindP(x 3).(Do not round intermediate calculations. Round final answer to 4 decimal places.)

P(x 3)

(e)FindP(x< 3).(Do not round intermediate calculations.Round final answer to 4 decimal places.)

P(x< 3) =P(x 2)

(f)FindP(x 4).(Do not round intermediate calculations.Round final answer to 4 decimal places.)

P(x 4)

(g)FindP(x> 2).(Do not round intermediate calculations. Round final answer to 4 decimal places.)

P(x> 2)

(h)Use the probabilities you computed in partbto calculate the mean _x, the variance,

2

x

x2, and the standard deviation, _x, of this binomial distribution. Show that the formulas for _x,

2

x

x2, and _xgiven in this section give the same results.(Do not round intermediate calculations. Round final answers to_xin to 2 decimal places,²_xand_xin to 4 decimal places.)

_x

2

x

x2_x

(i)Calculate the interval [_x 2_x]. Use the probabilities of partbto find the probability thatxwill be in this interval.Hint: When calculating probability, round up the lower interval to next whole number and round down the upper interval to previous whole number.(Round your answers to 4 decimal places. A negative sign should be used instead of parentheses.)

The interval is [,].P(x) =