Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.33 and a standard deviation of 1.5. U
1 answer:
"97.5" will be the American women's % having their shoe sizes that are no more than 11.33.
Given values are:
- Mean = 8.33
- Standard deviation = 1.5
Now,
=
= (2 above Standard deviation)
→ The data values are between 8.33 and 11.33,
=
= (%)
→ The data value below 11.33,
= (%)
hence,
→ The percentage of American women will be:
=
= (%)
Thus the above answer is appropriate.
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Given that the jeweler has alloys that are 25% gold, 50% gold, and 82% gold.
As he wants to make 14 grams of an alloy by adding two different alloys that is precisely 75% gold, so one alloy must have a percentage of gold more than 75%.
One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.
Case 1: 82% gold + 50% gold
Let x grams of 82% gold and y grams of 50% gold added to make x+y=14 grams of 75% gold, so
75% of 14 = 82% of x + 50% of y
[as x+y=14]
grams
and grams.
Hence, 10.9375 grams of 82% gold and 3.0625 grams of 50% gold added to make 14 grams of 75% gold.
Case 2: 82% gold + 25% gold
Let x grams of 82% gold and y grams of 25% gold added to make x+y=14 grams of 75% gold, so
75% of 14 = 82% of x + 25% of y
grams
and grams.
Hence, 12.28 grams of 82% gold and 1.72 grams of 50% gold added to make 14 grams of 75% gold.