On the average, there are 500 mg of aspirin in an “Extra Strength” aspirin table

Question

On the average, there are 500 mg of aspirin in an “Extra Strength” aspirin tablet. Suppose the random variable assigning amount of aspirin in a tablet is normally distributed with standard deviation 30 mg.

What proportion of extra strength aspirin tablets can be expected to contain between 475 and 525 mg of aspirin?

If you purchase a 100-tablet bottle of extra strength aspirin, about how many of them would contain more than 530 mg of aspirin?

How much aspirin would a tablet have to contain to be in the top 5% of the aspirin content range?

Explanation / Answer

mean = 500 , std. deviation = 30

By central limit theorem,

P(475 < X < 525)

= P[( 475 - 500) / 30 < Z < ( 525 -500) / 30 ]

= P( -0.83 <Z < 0.83)

= 0.5953

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