Suppose we will flip a fair coin 100 times. Let X be the number of heads, and use a Normal distribution to approximate the distribution of X.

a. Apply the continuity correction:

P(42<= X<= 58)= P()
(b) Apply the continuity correction:

P(X > =50) = P( X >

(a) P (42 ≤ X ≤ 58) = 0.9108

(b) P (X ≥ 50) = 0.5398

Step-by-step explanation:

The random variable X is defined as the number of heads.

The probability of tossing a Heads in a single flip is, P (X) = p = 0.50.

The coin was flipped n = 100 times.

The random variable thus follows a Binomial distribution with parameters n and p.

As the sample size is too large (n > 30) and the probability of success is closer to 0.50, the binomial distribution can be approximated by the Normal distribution.

The mean of this distribution is: .

The standard deviation of this distribution is:

(a)

Compute the value of P (42 ≤ X ≤ 58) by applying the continuity correction as follows:

After applying the continuity correction the probability statement is:

The probability is:

*Use a z-table for the probability value.

Thus, the value of P (42 ≤ X ≤ 58) by applying the continuity correction is 0.9108.

(b)

Compute the value of P (X ≥ 50) by applying the continuity correction as follows:

After applying the continuity correction the probability statement is:

The probability is:

Thus, the value of P (X ≥ 50) by applying the continuity correction is 0.5398.

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2

"exterior angles = 360 / number of sides.

60 = 360 / sides

sides = 360 / 60

sides = 6"