Suppose that x has a binomial distribution with n = 50 and p = .6, so that μ = np = 30 and σ = np(1 − p) = 3.4641. calculate the following probabilities using the normal approximation with the continuity correction. (hint: 22 < x < 37 is the same as 23 ≤ x ≤ 36. round your answers to four decimal places.) g

Question:

Suppose that x has a binomial distribution with n = 50 and p = 0.6, so that μ = np = 30 and σ = np(1 − p) = 3.4641. Approximate the following probabilities using the normal approximation with the continuity correction. (Hint: 26 < x < 32 is the same as 27 ≤ x ≤ 31. Round your answers to four decimal places.)

(a)    P(x = 30)

(b)    P(x = 26)

(c)    P(x ≤ 26)

(d)    P(26 ≤ x ≤ 32)

(e)    P(26 < x < 32)

(a)    P(x = 30)=0.1113

(b)    P(x = 26)=0.8064

(c)    P(x ≤ 26)=0.9032

(d)    P(26 ≤ x ≤ 32)=0.6674

(e)    P(26 < x < 32)=0.5101

Step-by-step explanation:

Here , X has a binomial distribution with n= 50 and p=6

The mean is μ=np=50(0.6)=30

The standard deviation is

=>3.4641

(A)  P(x = 30)

=>

=>

=>

=>

=>

=>[=NORMSDIST(0.14)]-[=NORMSDIST(0.14)]

=>0.5557-0.4443

=>0.1113

(B)P(x = 26)

=>

=>

=>

=>

=>

=>[=NORMSDIST(1.30)]-[=NORMSDIST(-1.30)]

=>0.9032-0.0968

=>0.8064  

(c) P(x ≤ 26)

=>

=>

=>

=>

=>

=>[=NORMSDIST(1.30)]

=>0.9032

D)  P(26 ≤ x ≤ 32)

=>

=>

=>

=>

=>

=[=NORMSDIST(0.72)]-[=NORMSDIST(-1.30)]

=>0.7642 -0.0968

=>0.6674  

(E) P(26 < x < 32)

=>

=>

=>

=>

=>

=>[=NORMSDIST(0.43)]-[=NORMSDIST(-1.01)]

=>0.6664-0.1563

=>0.5101  

the answer is (2x+8)²= 16