Statistics and Probability Answers

As studied, the average number of hours spent by senior high school students for their online classes a week is 25 hours with a standard deviation of 4 hours. Assuming that the study is true and the data is normally distributed. Find the probability that a randomly selected senior high school srudent spends less than 21 hours or greater than 30 hours.

Consider all samples of size of 5 from this population:

2, 5, 7, 9, 10, 11, 12

Compute the population mean

Compute the population variance

Compute the population standard deviation

Compute the mean of the sampling distribution of the sample means

Compute the variance of the sampling distribution of the sample means.

Compute the standard deviation of the sampling distribution of the sample means.

An explosion in a liquefied natural gas tank undergoing repair could have occurred as the result of static electiricity, malfunctioning electiral equipments, an open flame in contact with the liner or purposeful action. Interviews with engineers who were analyzing the risks led to estimates that such an explosion would occur with probability 0.25 as a result of static electricity, 0.20 as a result of malfunctioning electric equipment, 0.40 as a result of an open flame, and 0.75 result of purposeful action. These interviews also yielded subjective estimates of the probabilities of the four causes of 0.30, 0.40, 0.15 abd 0.15, respectively. Based on all information, what is the most likely cause of the explosion and what is the probability of explosion?

1. A carton of 24 light bulbs includes two that are defecetive. If two of the bulbs are chosen at random, what are the probabilities that

a Neither bulb will be defective

b One of the bulbs will be defective

c Both bulbs will be defective

1. An auction house has two appraisers of pecious jewelry. The probability that the older of the two will not be available is 0.33, the probability that the other one wil not be available is 0.27, and the probability that both of them will not be available is 0.19. What is the probability that either or both of them will not be available?

An explosion in a liquefied natural gas tank undergoing repair could have occurred as the result of static electiricity, malfunctioning electiral equipments, an open flame in contact with the liner or purposeful action. Interviews with engineers who were analyzing the risks led to estimates that such an explosion would occur with probability 0.25 as a result of static electricity, 0.20 as a result of malfunctioning electric equipment, 0.40 as a result of an open flame, and 0.75 result of purposeful action. These interviews also yielded subjective estimates of the probabilities of the four causes of 0.30, 0.40, 0.15 abd 0.15, respectively. Based on all information, what is the most likely cause of the explosion and what is the probability of explosion?

A shipment of 100 bags of sugar is rumoured to have some bags that contain illegal drugs. Local customs officials decide to screen shipments by randomly testing 4 bags. If any are found to contain drugs, the whole consignment is seized.

Compute the probability that the shipment consisting of 95 bags of sugar and 5 bags of illegal drugs will be detected in this manner.

A pharmacy buys one box of 50 thermal scanners each from four

different companies. There are 8 defective scanners in the box from the first

company, 4 defective scanners from the second company, 3 defective

scanners from the third company, and 5 defective scanners from the fourth

company. If one scanner is taken from each box, what is the probability

that the scanners from the first and second companies are defective and

the scanners from the third and fourth companies are not?​

A basket contains 10 ripe apples and 5 unripe apple. If four apples are taken from the basket one after the other, determine the possible values of the random variable r representing the number of ripe bananas

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A random sample of n=70 measurements is obtained from a population with a mean 200 and standard deviation of 50.describe the sampling for the sample means by computing