Steel rods mandachand with a mean length of nomaly datributed with a standad dev

Question

Steel rods mandachand with a mean length of nomaly datributed with a standad devation of 0 03 am Complete parts (o) to d a) Whatl proportion oll rods has a length less than 23 9 cm? process, the lengths of the rods are Rlound to fouar decimal places as needed) Any rods that are short" than 23 79oilonger than 24 21 arodecardedWhat proposon of,od wil be deal pond to four decinal places as needed) (c)Using teresults of part tbl i 5000 rads aro mandacared in a day, how m she dd to plant manager-to Ue the anoer rom part b to idi anewer Round to the nearest integer as neoded) d an order comes in for 10,000 steel od, ro ed in a day, how many should the plant manager expect to dscard , how mary rods shedd he plant managerespect to mandachnerorder state' tut al rod, mntbeba..m ngon m and 24 1 am (Round uptothe nearest integu) Enter your answer in each of the answer boxes

Explanation / Answer

a)P(X<23.9)=P(Z<(23.9-24)/0.09)=P(Z<-1.1111)=0.1333

b)

P(X<23.79)+P(X>24.21)=1-P(23.79<Z<24.21)=1-P(-2.3333<Z<2.3333)=1-(0.9902-0.0098)=0.0196

c) expected number to discard=np=5000*0.0196=~98

d)

here P(23.9<X<24.10)=P(-1.1111<Z<1.1111)=0.8667-0.1333=0.7335

hence number to be manufactured =10000/0.7335=13634

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