A multiple choice test is composed of 10 questions. Each question has four possible answers, only one of the four possible answers is correct. A student randomly selects the answer for each question. Assume that all selections are independent. Let X count the student's number of correct answers on the test. a) What is the expected number of correct answers? Round your answer to the nearest tenth. b) What is the standard deviation of the number of correct answers? Round your answer to the nearest hundredth. c) What values of the random variable are within two standard deviations of the mean? d) What is the probability that the student answers exactly 4 questions correctly? Round your answer to the nearest ten- thousandth. e) If at least 6 questions must be answered correctly to pass the test, what is the probability that the student passes the test? Round your answer to the nearest ten-thousandth.

a)2.5

b) 1.37

c) -0.24, 5.24

d) 0.1460

e) 0.0420

Step-by-step explanation:

Given:

n = 10

P = 1/4 = 0.25

a) expected number of answers

= n * p

= 10 * 0.25 = 2.5

b) standard deviation

= 1.37

c)• u-26 = 2.5 - 2(1.37)

= 2.5 - 2.75

= -0.24

• u+26= 2.5 + 2(1.37)

= 5.24

d) Pobability that the student answers exactly 4 questions correctly

= 0.1460

e) P(x≥6)=P(x=6)+P(x=7)+P(x=8)+P(x=9)+P(x=10)

= 0.03845+0.00309+0.00039+0.0000286+0.000000954

= 0.0420

(Part (e) is also attached for easier understanding)

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.