In this economically challenging time, yours truly, CEO of the Outrageous Produc

Question

In this economically challenging time, yours truly, CEO of the Outrageous Products Enterprise, would like to make extra money to support his frequent filet-mignon-anddouble-lobster-tail dinner habit. A promising enterprise is to mass-produce tourmaline wedding rings for brides. Based on my diligent research, I have found out that women's ring size normally distributed with a mean of 6.0, and a standard deviation of 1.0. I am going to order 5000 tourmaline wedding rings from my reliable Siberian source. They will manufacture ring size from 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, and 9.5. How many wedding rings should I order for each of the ring size should I order 5000 rings altogether? (Note: It is natural to assume that if your ring size falls between two of the above standard manufacturing size, you will take the bigger of the two.)

Explanation / Answer

We will use the empirical rule to solve this question. By empirical rule we know that 68.27 % of data lies within one standard deviation, 95.45% of data lies within two standard deviation and 99.73% of data lies within 3 standard deviations.

68.27% of 5000 is 3414.

95.45% of 5000 is 4772

99.73% of 5000 is 4986

I have rounded up the values so that they are even so that they may be distributed symmetrically.

Thus 3414 rings should be made of the size 6.0.

Number of rings of size 5.5/6.5 =(4772-3414)/2 = 679.

Thus 679 rings should be made of size 5.5 and 679 rings of size 6.5.

Number of rings of size 5.0/7.0 = (4986-4772)/2 = 107

Thus 107 rings of size 5.0 should be made and 107 rings of size 7.0 should be made.

For the remaining 4 rings 2 rings of size 4.5 and 2 rings of size 7.5 should be made.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.