A company that makes hair-care products had 7,000 people try a new shampoo. Of the 7,000 people, 56 had a mild allergic reacti
on. What percent of the people had a mild allergic reaction?
2 answers:
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Given that normally distributed data set has a mean of 55 and 99.7% of data fall between 47.5 and 62.5.
Let s be the standard deviation of data set.
Since 99.7% data fall within 3 standard deviations of mean, z-value for 47.5 and 62.5 has an absolute value of 3.
That is |z|=3
But z=
Let us plugin x=47.5 and mean =55 and equate it to 3.
That is
Since x is always positive ( being standard deviation),
Hence
We will get same value with 62.5 as well.
Hence standard deviation of data set is 2.5.