Search & Filtering
Referring to the random variables whose joint probability distribution is given
One sample has n = 4 scores and M = 10. A second sample has n = 6 scores and M = 5. If the two samples are combined, then what is the mean for the combined sample?
In a city, it is estimated that the maximum temperature in June is normally distributed with a mean of 28º and a standard deviation of 5.4°. Calculate the number of days in this month in which it is expected to reach a maximum of between 22° and 31°.
In a class of 28 students, 21 have a cat and 9 have a dog. There are 7 students who have a cat and a dog. What is the probability that a student has a dog given that they do not have a cat?
In a certain Algebra 2 class of 28 students, 7 of them play basketball and 5 of them play baseball. There are 18 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
The mean weight of 800 college students is 56 kg and the standard deviation is 5 kg. Assuming that the weight is normally distributed, determine how many students weigh:
In a poker hand consisting of 5 cards, find the probability of holding (a) 3 kings; (b) 4 red cards and 1 club.
The birth weight of babies is normally distributed with a mean of 3.5 kg. A researcher
suspects that the weight of babies from mothers who were alcoholics during their
pregnancy will have a lower weight compared to the population mean. A random
sample of 40 babies from such mothers who drank a lot of alcohol were examined. The
mean birth weight in this sample was 3.2 kg with a standard deviation of 0.5 kg.
i. Would you conclude that the researcher’s claim is true at a 1% significance level?
ii. Make a 94% confidence interval for the mean birth weight of all babies.
A computer system analyst claims that the average number of fatal system errors that
occurred is at most 52.3 cases per day. The general manager wants to check if this
claim is true. A random sample of 100 computers taken by the general manager showed
that these computers have an average of 48.9 fatal system errors that occurred per day
with a variance of 64.
a) What is the point estimate of the population mean?
b) Find a 92% confidence interval for the corresponding population mean.
Leave your answer in 1 decimal place.
c) What is the conclusion that can be made by the general manager on the system
analyst’s claim at 2.5% significance level?
According to an officer in the Health Care Financing Administration, the average
annual expenditure on toiletries is RM110 per person in Malaysia. The data of 30
randomly selected persons are as follows and the standard deviation of the sample is
19.2152.
125 110 110 90 90
85 125 110 85 120
130 125 130 90 130
80 120 90 110 90
90 85 100 130 80
90 100 125 150 100
i. Find the sample mean of the data.
ii. Is there enough evidence to support the officer’s claim at 0.02 level of significance?
iii. What is the decision at a 0.2% significance level?
