Math Answers

Find the area under the normal curve in each of the following cases. between z = 0 and z = 1.63 between z= 0 and z = 1.78 between z = -2.46 and z = 1.55 to the right of z = 2.35 to right of z = -1.31 to the left of z = 0.35 to the left of z - 1.85 to the right of z = -0.95

If 1.6 accidents can be expected an intersection on any given day, what is the

probability that there will be 3 accidents on any given day?

The annual wages X of the staffs of collage of natural sciences are normally

distributed with mean µ and standard deviation σ. Knowing that P(X > 42320) =

0.0853 and P(X < 41230) = 0.6103, find µ and σ.

Suppose that an examination consists of six true and false questions, and assume that

a student has no knowledge of the subject matter. The probability that the student will

guess the correct answer to the first question is 30%. Likewise, the probability of

guessing each of the remaining questions correctly is also 30%.

a. What is the probability of getting more than three correct answers?

b. What is the probability of getting at least two correct answers?

c. What is the probability of getting at most three correct answers?

d. What is the probability of getting less than five correct answers

A ball is drawn at random from an urn containing one red and one white ball. If the

white ball is drawn, it is put back into the urn. If the red ball is drawn, it is returned to

the urn together with two more red balls. Then a second draw is made. What is the

probability a red ball was drawn on both the first and the second draws?

A box of 80 candles consists of 30 defective and 50 non defective candles. If 10 of

this candles are selected at random by business man for sale, what is the probability

a. All will be defective

b. 6 will be non-defective

c. All will be non-defective

Two dice are rolled. Let X be a random variable denoting the sum of the numbers on

the two dice.

i) Give the probability distribution of X

ii) Compute the expected value of X and its variance

Among 15 clocks there are two defectives. In how many ways can an inspector chose

three of the clocks for inspection so that:

a. There is no restriction.

b. None of the defective clock is included.

c. Only one of the defective clocks is included.

d. Two of the defective clock is included.

A package contains 12 resistors, 3 of which are defective. If 3 are selected, find the probability of getting

(a) no defective resistor.

(b) one defective resistor.

(c) all defective resistors 

a) Determine the missing frequencies of the following distribution given that the median

is 33.5 and themode is 34.0.

Class limits 0-9 10-19 20-29 30-39 40-49 50-59 60-69 Total

Freq. 4 16 f3 f4 f5 6 4 230

b) Compute the arithmetic mean.

c) Compute the value below which 25% of the observations lie.

d) Compute the value above which 25% of the observations lie