MATH 1131 Lecture Notes - Lecture 8: Point Estimation, Statistical Parameter, Confidence Interval

1)

The inside diameter of a randomly selected piston ringis a random variable with mean value 11 cm and standard deviation0.02 cm. Suppose the distribution of the diameter is normal. (Roundyour answers to four decimal places.)

(a) Calculate P(10.99 ? X ? 11.01) when n =16.

(b) How likely is it that the samplemean diameter exceeds 11.01 when n =25?

2)

Suppose the sediment density (g/cm) of a randomlyselected specimen from a certain region is normally distributedwith mean 2.7 and standard deviation0.85.

(a) If a random sample of 25 specimensis selected, what is the probability that the sample averagesediment density is at most 3.00? Between 2.7 and 3.00? (Round your answers to four decimalplaces.)

at most 3.00 = ?

between 2.7 and 3.00 =?

(b) How large a sample size would berequired to ensure that the probability in part (a) is at least0.99? (Round your answer up to the nearest whole number.)

3)

The inside diameter of a randomly selected piston ringis a random variable with mean value 10 cmand standard deviation 0.05cm.

(a) If X isthe sample mean diameter for a random sample of n = 16rings, where is the sampling distribution of

(b) Answer the questions posed in part (a)for a sample size of n = 64 rings. (Enter your standarddeviation to five decimal places.)

center = ?

standard deviation = ?

A population variable has a distribution with mean u= 50 and variance o = 225. From this population a simple random sample of n observations is to be selected and the mean of the sample values calculated. 6. If the population variable is known to be Normally distributed and the sample size used is to be n = 16, what is the probability that the sample mean will be between 48.35 and 55.74, i.e., P(48.35 s I s 55.74)? A) 0.393 B) 0.607 C) 0.937 D) 0.330 E) Not within +0.010 of any of the above.

The queuing time at an airline check-in has a population mean h = 13 minutes and variance o2 = 16 minutes2. Suppose that n = 27 passengers were randomly selected from this population. They were interviewed and reported the queued times. Let x̄ defines the sample mean of n observations. Answer the followings:

a) Define your random variable X.

b) Define the sampling distribution of sample mean (indicate a reason and give the name of the distribution, the parameters and sketch it.

c) What is the probability that a sample mean is at most 11 minutes. Please skecth the problem and show all details of your answer.

d) Suppose that for n = 27 passengers, the sample mean is observed as x̄= 10 minutes. Based on part c, can we claim that the population mean queuing time is less than 13 minutes.

e) Construct a 95% acceptance region for sample mean of queing time (i.e., u + za x f) Interpret the result obtained in parte and skecth the control chart.