ASSIGNMENT QUESTION

QUESTION 1

A light bulb is advertised as lasting an average of 1000 hours with a standard deviation of 150 hours. Find the probability of buying a light bulb that will last:
a) Between 1000 and 1250 hours
b) More than 1250 hours
c) Between 901 and 1000 hours
d) Between 901 and 1250 hours

QUESTION 2
Records in an insurance company show that the mean payout for all automobile claims is RM1800 and the standard deviation is RM400. Suppose 20 claims are filed in a week and X, the payout for an automobile follows a normal distribution.

a) If the sample mean X¯ is chosen as a point estimator for the population mean μ. Determine whether X¯ is an unbiased estimator for μ.

b) Determine the sampling distribution for the sample mean, X¯ and calculate the mean and the standard deviation for X¯.

QUESTION 3

To investigate the proportion of smokers who believe that smoking should be banned from public buildings, a researcher randomly samples 500 adult smokers. He finds that 155 smokers support that idea. Obtain a 99% confidence interval for the true proportion of smokers who believe that smoking should be banned from public buildings. Find the sample size necessary to reduce the maximum error to 0.03 with a 99% confidence.

QUESTION 4

The daily yield for a local chemical plant has averaged 880 tons for several years. The quality control manager would like to know if this average has changed .He randomly selects 50 days and records an average yield of 871 tons with a standard deviation of 21 tons. Conduct the test using α = 0.05.

QUESTION 5

The lifespan of a fax machine X is normally distributed. The lifespan (in thousand hours) of a random sample of ten fax machines X is recorded as follows:

(a) Determine the point estimators (in thousand hours) for the above data.

(b) Construct a 95% confidence interval for the true mean lifespan of X.