Question

The owners of the Burger Emporium are looking for new supplier of onions for their famous hamburgers. It is important that the onion slice be roughly the same diameter as the hamburger patty. After careful analysis, they determine that they can only use onions with diameters between 9 and 10 cm. Company A provides onions with diameters that are approximately normally distributed with mean 10.3 cm and standard deviation of 1.2 cm. Company B provides onions with diameters that are approximately normally distributed with mean 10.6 cm and standard deviation of 0.9 cm. Which company provides the higher proportion of usable onions? Justify your choice with an appropriate statistical argument using proportions.

Answer 1

Answer:

Follows are the solution to this question:

Step-by-step explanation:

Let assume that X and Y reflect the diameters of onions by companies A and B.

$\to P(9<X<10) = P(\frac{9-10.3}{1.2} < Z < \frac{10-10.3}{1.2} )$

                          $= P(-1.0833 < Z < -0.25)\\\\= P(Z < -0.25) - P(Z<-1.0833)\\\\= 0.2620$

$\to P(9<Y<10) = P(\frac{9-10.6}{0.9} < Z < \frac{10-10.6}{0.9} )$

                          $= P(-1.7778 < Z < -0.6667)\\\\= 0.2148$

As a result, onions through company A are chosen and they're more likely to be accepted.