Math Answers

A spring of natural length 10 in. stretches 1.5 in. under a weight of 8 lb. Find the work done in stretching the spring

(a) from its natural length to a length of 14 in.

(b) from a length of 11 in. to a length of 13 in.

Let f be a differentiable function on ] [α, β and ]. x ∈[α, β Show that, if 

f ′(x) = 0 and ,0 f ′′(x) > then f must have a local maximum at x.

What is meant by the following measures of position below?

1. Q₃ = 94

2. D₈ = 17

3. P₉₀ = 42

A population consists of 3, 6, 9, 12, 15, and 18. If random samples of

size 3 will be drawn from this population, what will be the mean of the

sampling distribution of the sample means?

Analyze and solve the following problems.

a. What is the probability that when you roll a die, the outcome is an even number?

b. What is the probability that when you determine the blood type of an individual his or her blood type is type O?

c. In a standard deck of cards, what is the probability of drawing a card that is a heart or an ace?

d. A coin is tossed thrice. What is the probability of obtaining exactly 2 heads occur?

e. According to the recent news, the probability of raining today is 65%. What is the probability of not raining today?

State the sample space for each other of the following random experiments.

a. tossing a coin

b. rolling a die

c. number of male children in a family of 2 children

d. identifying the blood type of an individual

e. determine the civil status of an individual

Suppose the random variable X has the uniform distribution on the integers 10,11,12

......,30 Find probability that X is the prime number

1.      The prices for LED are listed: 22 500, 24 000, 21 500, 20 200, 20 600, 21 100, 210 000, 19 300, 25 000 and 22 500. Estimate the true mean of the data set with 90% confidence level.

1.      Find the sample size to estimate a population mean within 95% confidence if the standard deviation is 6.2.

1.      A study of 40 SHS English teachers established that they spent 12.6 minutes revising a student’s term paper.

a. Find the 90% confidence interval in the mean time for all composition papers when minutes.

b. If the teacher affirmed that she spent an average of 30 minutes revising a term paper, what would be your reaction?