Search & Filtering
Suppose that the monthly incomes of all employees in Firm A are normally distributed with a mean of $1784.85 and a standard deviation of $199.23. If a random sample of 121 employees is selected from Firm A, what is the probability that the mean of the employees in the sample will be greater than $1809.572632 (approximately)?
A dry-cleaning establishment claims that a new spot remover will remove more than 80% of the spots to which it is applied. To check this claim, the spot remover will be used on 12 spots chosen at random. If fewer than 11 of the spots are removed, we shall not reject the null hypothesis that p = 0.8; otherwise, we conclude that p > 0.8
(i) Evaluate α , assuming that p = 0 .8 (ii) Evaluate β for the alternative p = 0.9.
The number of computer malfunctions per day is recorded for 260 days with the
following results.
Number of malfunctions (x i ) 0 1 2 3 4 5
Number of days(f i ) 77 90 55 30 5 3
Test the goodness of fit of an appropriate probability model.
Find the regression line of y on x for the following data:
X 40 70 50 60 80 50 90 40 60 60
Y 2.5 6.0 4.5 5.0 4.5 2.0 5.5 3.0 4.5 3.0
Draw the line. Estimate the value of y when x = 10.
Calculate the mean and standard deviation for the following data:
Neck circumference
(in inches)
12 12.5 13 13.5 14 14.5 15 15.5 16
Frequency
5 20 30 43 60 56 37 16 3
The formula for the standard error (standard deviation of the distribution of sample means) implies that as the sample size (n) increases, the size of the standard error decreases. Explain the role of the standard error in comparing the sample mean and the population mean. Use the definitions and concepts on sample means distribution and standard error and show examples comparing the sample mean and the population mean of a distribution when the standard error changes in value to express your answer
The mean annual cost to attend a college is $44,324. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,590.
Ninety percent of all students pay less than what amount?
Forty-five percent of the streets in an area have private guards for security. Three streets are selected at random:
i. What is the probability all three of the selected streets have private guards?
ii. What is the probability none of the three selected streets has private guards?
iii. What is the probability at least one of the selected streets has private guards?
iv. What is the probability at most two of the selected streets have private guards?
The formula for the standard error (standard deviation of the distribution of sample means) implies that as the sample size (n) increases, the size of the standard error decreases. Explain the role of the standard error in comparing the sample mean and the population mean. Use the definitions and concepts on sample means distribution and standard error and show examples comparing the sample mean and the population mean of a distribution when the standard error changes in value to express your answer
Weights of newborn babies in a particular city are normally distributed with a mean of 3380 g and a standard deviation of 475 g.
a. A newborn weighing less than 2100 g is considered to be at risk, because the mortality rate for this group is very low. If a hospital in the city has 500 births in a year, how many of those babies are in the “at-risk” category?
b. If we redefine a baby to be at risk if his or her birth weight is in the lowest 3%, find the weight that becomes the cutoff separating at-risk babies from those who are not at risk.
c. If 20 newborn babies are randomly selected as a sample in a study, find the probability that their mean weight is between 3200 g and 3500 g.
