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If a binomial distribution has 10 trials and the probability of success is 0.4, then the mean is


Tom has a 0.5 chance of winning the Booker Prize, whereas John has a 0.4 chance of winning the Booker Prize. Only one Booker prize is up for grabs. How likely is it that at least one of them will win the prize?


Tom has a 0.5 chance of winning the Booker Prize, whereas John has a 0.4 chance of winning the Booker Prize. Only one Booker prize is up for grabs. How likely is it that at least one of them will win the prize?


Let X be the number of life years before certain kind of CFL bulb needs replacement . Let X have the probability mass function is defined as

f(x)=alphax**3,x=0,1,2,3,4

Where alpha is constant

(a) Find the values of constant alpha

(b) find the cumulative distribution function F to X



The professional organization for private colleges and universities


professors reported that more than 17% of professors attended a


national convention in the past year. To test this claim, a researcher


surveyed 200 professors and found that 45 has attended a national


convention in the past year. At 𝛼 = 0.05, test the claim that this figure


is correct using p -value method.

The school registrar estimates that the dropout rate of freshmen high schools in Mindanao


is 20%. Last year, 45 freshmen from a random sample of 250 Mindanao freshmen high


school withdrew. At 𝛼 = 0.01, is there enough evidence to reject the registrar’s claim?

Let X be a random variable with the following probability distribution:





x 1 2 3 4




P(X) 0.4 0.3 0.2 0.1




Find the expected value and variance.

A survey of Davao Region finds the average commute time of employees on one way is 30


minutes. The Digos Chamber of Commerce feels that in their city is greater and want to


publicize this. They randomly select 28 commuters and find the average is 35 minutes with


a standard deviation of 6 minutes. At 𝛼 = 0.05, are they correct?

The school registrar estimates that the dropout rate of freshmen high schools in Mindanao




is 20%. Last year, 45 freshmen from a random sample of 250 Mindanao freshmen high




school withdrew. At 𝛼 = 0.01, is there enough evidence to reject the registrar’s claim?

A survey of Davao Region finds the average commute time of employees on one way is 30



minutes. The Digos Chamber of Commerce feels that in their city is greater and want to



publicize this. They randomly select 28 commuters and find the average is 35 minutes with



a standard deviation of 6 minutes. At 𝛼 = 0.05, are they correct?

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