normally distributed with a standard deviation of 0.06 am (a) what proportion of

Question

normally distributed with a standard deviation of 0.06 am (a) what proportion of rods has a length less than 29.9cm? (Round to four decimal places as needed.) (b) Any rods that are shorter than 29.88 cm or longer than 30.12 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? a standard deviation of 0.06 cm. Complete parts (a) to (d nts (Use the answer from part b to find this answer. Round to the nearest integer as needed.) that all rods must be between 29.9cm (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 and 30.1 cm? (Round up to the nearest integer.) 17212

Explanation / Answer

Sol:

mean=30

sd=0.06

P(X<29.9)

z=x-mean/sd

Z=29.9-30/0.06

Z=-1.66667

pnorm(-1.66667)

=0.04779002

ANSWER:0.0478

Solutionb:

P(29.88<x<30.12)

P(29.88-30/0.06<Z<30.12-30/0.06)

P(-2<Z<2)

P(Z<2)-P(Z<-2)

pnorm(2)-pnorm(-2)

0.9544997

0.9545

ANSWER:0.9545

Solutionc:

np=5000*0.9544997

= 4772.498

=4772

ANSWER:4772

Solutiond:

P(29.9<X<30.1)

P(29.9-30/0.06<Z,30.1-30/0.06)

P(-1.67<Z<1.67)

0.9050806

np=10000* 0.9050806

=9050.806

answer:9051

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