Statistics and Probability Answers

In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses resulted in a mean of 96,700 miles and a standard deviation of 37,500 miles. At the 0.05 level of signıficance, test the manufacturer's claim that the mean distance traveled before a major engine failure is more than 90,000 miles.

1. Claim:

Ho:

Ha:

2. Level of Significance:

Test- statistic:

Tails in Distribution:

3. Reject Ho if:

4. Compute for the value of the test statistics.

5. Make a decision:

6. State the conclusion in terms of the original problem.

Which statements below are true and which are false? Give a reason for your answer. If the median mass of five chemical reagent bags in the store room is 6.5 kg and one further 7 kg bag of chemical reagent is added to the consignment, then: (a) the new median mass will be about 6.6 kg (b) the median will increase (c) it is impossible for the new median mass to be less than it was (d) it is impossible for the new median mass to stay exactly at 6.5 kg (e) the median may increase, but that depends on the actual masses of all five parcels.

Five hundred children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. What is the probability that the height of a child, picked at random, is greater than 104 cm?

The weights of 1,000 children average is 50 kg and the standard deviation is 5 kg. How many children weigh between 40 kg and 55 kg?

The packaging of an electric light bulb states that the average length of life of bulbs is 1000 hours. A consumer association thinks that this is an overestimate and tests a random sample of 64 bulbs, recording the life 𝒙 hours, of each bulb. The results are summarized as follows:

∑ 𝒙 = 𝟔𝟑𝟗𝟏𝟎. 𝟒 and ∑ 𝒙

𝟐 = 𝟔𝟑𝟖𝟐𝟒𝟎𝟔𝟏

Which statements below are true and which are false? Give a reason for your answer. If the median mass of five chemical reagent bags in the store room is 6.5 kg and one further 7 kg bag of chemical reagent is added to the consignment, then: (a) the new median mass will be about 6.6 kg (b) the median will increase (c) it is impossible for the new median mass to be less than it was (d) it is impossible for the new median mass to stay exactly at 6.5 kg (e) the median may increase, but that depends on the actual masses of all five parcels.

1.     A café is introducing three sets of healthy menu named S1, S2 and S3.   On the first day, the number of plates prepared for each set depends on the time of the day. Set 1, 2 and 3 are prepared in the amount of 30%, 20% and 50% respectively. At the end of the day, the number of leftovers (L) for the three set is as follows:

p(L l S1) = 0.01 , P(L l S20 = 0.03 , P(L lS3) = 0.02

If a random leftover plate was selected,

i.                   Discuss how you would find the set that will likely has the most leftovers

ii.                  Which set is most likely to have the most leftovers? 

1.     The students at a swimming class consists of 10 girls, 30 boys and 10 adults. After a month lesson, 3 of the girls, 10 of the boys and 3 of the adults were able to swim. If a student is chosen at random from this class and is found to be able to swim, what is the probability that the student is a boy?

Suppose three laptops are tested.Let D represent the defective laptop and N for the non defective laptops.how many possible outcomes will occur from the experiment and what are the possible values of the random variable?

A real estate agent has 8 master keys to open several new homes. Only 1 master

key will open any given house. If 40% of these homes are usually left unlocked, what

is the probability that the real estate agent can get into a specific home if the agent

selects 3 master keys at random before leaving the office?