Math Answers

A continuous random variable is normally distributed with a mean of 45 and standard deviation 0f 6. Illustrate the following notations in a normal curve.

P( 30 < X < 50 )

P( 33 ≤ X ≤ 39)

P( X < 57 )

A random variable X has a normal distribution with mean 45 and variance of 9.

Find the range of scores that lie:

a. within one standard deviation from the mean

b. within two standard deviations from the mean

scores on acommon final examination in alarge enrollment, multiple selection freshman course are normally distributed with a mean of 72. 7 and standard deviation of 13.1 a. Find the probability that the score X on a randomkly selected examination paper is between 70 and 80

C. Find the probabilities on a standard normal curve.

1. P(-3.0 ˂ z < -1.68)

2. P(-2.76 < z < 2)

3. P(1.53 < z < 2)

Find each of the following percentile points and draw the appropriate normal

curve. Complete your procedures.

1.The results of the entrance examination for freshmen are normally distributed with x=87 and s=12.5. What is the percentile rank of a score of 90?

We take a random sample of 60 households to estimate the percentage of all

homes in the Spring Town Village that have a refrigerator. It turns out that 49 of

the 60 homes in our sample have a refrigerator. Use 95% confidence level to

calculate the length of confidence interval estimation of population proportion of

households with refrigerator.

A bottled water company has found in the past that 2% of their bottled water does not meet the company’s high standards. As such periodic samples are taken and tested for their quality. If from the last batch a sample of 12 bottles are taken and tested, determine the probability:

i. Carefully defining the random variable of interest [1]

ii. What is the probability distribution? State the values of the parameters [2]

iii. Justifying the suitability of the probability distribution identified in part (ii) [4]

iv. Calculate the probability that at most 2 bottles do not meet the company’s Standards [4]

v. The expected number of bottles that do not meet the company’s standards. [2]

vi. The amount of sodium sulfate, in mg, found in the bottled water follows a normal distribution with a mean 13mg and a standard deviation of 2.5mg. It is known that 76% of the bottles have a mean that is more than x mg. Find the value of x

If P (A) = 1/3

, P (B^c) = 1/4

, then P (AB) = 0.

True or False?

A population consist of 2,4,5,9 and 10, with sample size of 3. Compute the mean and variance of the

sampling distribution of the sample mean.

The total number of hours, measured in units of

100 hours, that a family runs a vacuum cleaner over a

period of one year is a continuous random variable X

that has the density function

f(x) =

⎧

⎨

⎩

x, 0 2 − x, 1 ≤ x < 2,

0, elsewhere.

Find the variance of X.

Find the average number of hours per year that families run their vacuum cleaners.