Question 2 A binomial probability experiment is conducted wi

Question 2

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.

N=10, p=0.7, x=5

P (5) =?

(Do not round until the final answer. Then round to four decimal places as needed)

Question 3

Determine the area under the standard normal curve that lies between (a) Z = - 0.05 and Z = 0.05, (b) Z = - 1.91 and Z = 0, and Z = - 0.47 and Z = - 0.21.

a. The area that lies between Z= - 0.05 and Z = 0.05 is?

(Round to four decimal places as needed)

b. The area that lies between z = - 1.91 and Z = 0 is?

(Round to four decimal places as needed)

c. The area that lies between Z = - 0.47 and Z =- 0.21 is?

(Round to four decimal places as needed)

Solution

(2) Given X follows Binomial distribution with n=10 and p=0.7

P(X=x)=10Cx*(0.7^x)*(0.3^(10-x)) for x=0,1,2,...,10

P(X=5) = 10C5*(0.7^5)*(0.3^(10-5)) =0.1029

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(3)a. The area that lies between Z= - 0.05 and Z = 0.05 is?

P(-0.05<Z<0.05) =0.0399 (from standard normal table)

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b. The area that lies between z = - 1.91 and Z = 0 is?

P(- 1.91<Z<0) =0.4719 (from standard normal table)

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c. The area that lies between Z = - 0.47 and Z =- 0.21 is?

P(- 0.47<Z<- 0.21) =0.0977 (from standard normal table)