please complete all parts, im confused! Question Help Steel rods are manufacture

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please complete all parts, im confused!

Question Help Steel rods are manufactured with a mean length of 24 centmeler (em) Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.09 cm. Complete parts (a) to (d) (a) What proportion of rods has a length less than 23.9 cm? (Round to four decimal places as needed ) (b) Any rods that are shorter than 23 78 cm or longer than 24 22 cm are discarded. What proportion of rods will be discarded? (Round to four decimal places as needed ) (c) Using the results of part (b), if 5000 rods are manufactured in a day, how many should the plant manager expect to discard? (Use the answer from part b to find this answer Round to the nearest integer as needed) (d) If an order comes in for 10.000 steel rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 23 9 cm and 24.1 cm? (Round up to the nearest rte ger ) Enter your answer in each of the answer boxes D Related Blogs SAT-Free Practice Tests 20/2049 Mesthew5

Explanation / Answer

P(X < A) = P(Z < (A - mean) /standard deviation)

A) P(X < 23.9) = P(Z < (23.9 - 24)/0.09)

= P(Z < -1.11)

= 0.1335

B) P(X < 23.78) = P(Z < (23.78-24)/0.09)

= P(Z < - 2.44)

= 0.0073

P(X > 24.22)

= 1 - P(Z < 2.44)

= 0.0073

P(23.78 < X < 24.22) = 0.0073 + 0.0073 = 0.0146

C) Expected number to be discarded = 0.0146x5000 = 73

D) P(23.9 < X < 24.1) = 1 - 0.1135x2

= 0.733

Expected number of rods to be manufactured = 10,000/0.733

= 13643

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