Statistics and Probability Answers

A fair die is rolled till all the numbers 1, 2, ..., 6 appear on the top. What is the probability that at least 7 rolls are needed?

The Coronavirus Disease (COVID-19) is an infectious disease caused by a new strain of

coronavirus. The World Health Organization (WHO) claims that the incubation period of the virus

in the infected person has a mean of 5.1 days with a standard deviation of 3.32. The doctors in the Philippines conducted a research and they found out that incubation period of the virus in human body is 6.03 days. The samples were 46 COVID patients. Is there enough evidence to

conclude that the incubation period of the virus is 5.1 days as stated, at 𝛼 = 0. 01?

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 a child picked at random has a height less than 104 cm?

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 a child picked at random has a height greater than 116 cm?

Five hundred children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. How many children belong to the upper 15% of the group?

Five hundred children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. How many children have heights between 98 cm and 104 cm?

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 a child picked at random has a height fewer than 95 cm or more than 130 cm?

A manufacturer claims that the average weight of a tin of baked beans in 440g and the standard deviation is known to be 20g. From a random sample of 100 cans you calculate the average weight to be 435g. At the 95% level of confidence, is there a change in the average weight of a can of baked beans?

The Coronavirus Disease (COVID-19) is an infectious disease caused by a new strain of 

coronavirus. The World Health Organization (WHO) claims that the incubation period of the virus 

in the infected person has a mean of 5.1 days. The doctors in the Philippines conducted a 

research and they found out that incubation period of the virus in human body is 6.03 days with a 

standard deviation of 3.32. The samples were 46 COVID patients. Is there enough evidence to 

conclude that the incubation period of the virus is 5.1 days as stated, at 𝛼 = 0. 01?

Suppose that the annual income of a fast-food chain is normally distributed with a mean of $72,000 and a standard deviation of $9,000.

a. What is the probability that a randomly selected fast-food restaurant will generate an annual income between $65,000 and $75,000?

b. What is the probability that a randomly selected fast-food restaurant will generate an annual profit of more than $80,000?

c. What minimum income does a fast-fast restaurant need to earn to be in the top 5% of incomes?

d. What maximum income does a fast-food restaurant need to earn to be in the bottom 30% of incomes?