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ox File Edit View History Bookmarks Tools Window Help tud 167 MTH 240-41H Samantha Wallace 12/2/17 10:50 PM Quiz: Ch 7 Quiz Submit Quiz This Question: 4 pts This Quiz:42 pts possible Steel rods are normally distributed with a standard deviation of 0.07 cm. Complete parts (a) to (d) with a mean length of 28 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods ane (a) What proportion of rods has a length less then 27.9 cm? (Round to four decimal places as needed.) (b) Any rods that are shorter than 2783 om or longer than 28.17 cm are discarded. What proportion of rods will be discarded? ook chl ( (Round to four decimal places as needed.) (e) Using the results of part (b), 5000 rods are manufactured in a day, how many should the plant manager expect to (Use the answer from part b to find this answer. Round to the nearest integer as needed.) cm and 28.1 cm? D:Round up to the nearest integer.) or expect to manufacture if the order states that all rods must be between 27.9 d( If an order comes in for 10,000 stoel rods, how many rods should the plant manager se

Explanation / Answer

Mean = 28

Sd = 0.07

A) P(X < 27.9) = P(Z < (27.9 - 28)/0.07)

= P(Z < - 1.43)

= 0.0764

B) P(27.83 < Z < 28.17) = P((27.83-28)/0.07 < Z < (28.17-28)/0.07)

= P(-2.43 < Z < 2.43)

= P(Z < 2.43) - P(Z < - 2.43)

= 0.9925 - 0.0075

= 0.9850

C) n = 5000

Expected value = 5000 * 0.985 = 4925

D) P(27.9 < X < 28.1) = P((27.9 - 28)/0.07 < Z < (28.1-28)/0.07)

= P(-1.43 < Z < 1.43)

= P(Z < 1.43) - P(Z < - 1.43)

= 0.9236 - 0.0764

= 0.8472

n = 10000

Expected value = 10000 * 0.8472 = 8472

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