00:01
In the manufacturing process of an antihistamine drug, the mean amount of the active ingredient in the tablet is 10 .2 and the standard deviation is 0 .81.
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The company has received an order of this drug with specifications of 9 mg to 11 mg.
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We're to find the percentage of tablets expected to be below the specification limits, above the specification limit and within the specification limit.
00:31
And lastly, the company wants to have at least 97 % of the product within the specification limit.
00:38
What should be the target standard deviation of the process to achieve this? so for the first one, the probability of below the specification, this would be, we have the range as 9 to 11.
01:00
So this would be the probability of x less than 9.
01:03
So this is p of x minus u over the standard deviation less than g, less than 9 minus 10 .2 divided by 0 .81.
01:20
So this would be p of z less than minus 1 .4815 using the z table and this gives us 0 .0692.
01:32
Now the probability of above the specification, this would be greater than x greater than 11...