# What is the value of a? P(X≥a)=0.5

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The value of ( a ) corresponds to the ( a )th percentile of the distribution of random variable ( X ), such that the probability of ( X ) being greater than or equal to ( a ) is 0.5.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A medical researcher says that less than #25%# of US. adults are smokers. In a random sample of #200# US. adults, #18.5%# say that they are smokers. At #alpha = 0.05#, is there enough evidence to reject the researchers claim?
- In a certain region, 46% of the population is female.It is known that 5% of males and 2% of females are left-handed.A person is chosen at random and found to be left-handed.What is the probability that this person is a male?
- If #P(A) = .7, P(B) = .5#, and #P(B|A)=.4#, what is #P(A# and #B)#?
- What is the value of a? P(X≥a)=0.5
- A medical researcher says that less than #25%# of US. adults are smokers. In a random sample of #200# US. adults, #18.5%# say that they are smokers. At #alpha = 0.05#, is there enough evidence to reject the researchers claim?

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