Question

# 1) A company produces steel rods. The lengths of the steel rods are normally distributed with...

1) A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 183.4-cm and a standard deviation of 1.3-cm.
Find the probability that the length of a randomly selected steel rod is between 179.9-cm and 180.3-cm.
P(179.9<x<180.3)=P(179.9<x<180.3)=

2) A manufacturer knows that their items have a normally distributed length, with a mean of 6.3 inches, and standard deviation of 0.6 inches.
If 9 items are chosen at random, what is the probability that their mean length is less than 5.9 inches?

1)

 for normal distribution z score =(X-μ)/σx here mean=       μ= 183.4 std deviation   =σ= 1.3

probability that the length of a randomly selected steel rod is between 179.9-cm and 180.3-cm :

 probability =P(179.9

2)

 here mean=       μ= 6.3 std deviation   =σ= 0.60 sample size       =n= 9 std error=σx̅=σ/√n= 0.20000
 probability =P(X<5.9)=(Z<(5.9-6.3)/0.2)=P(Z<-2)=0.0228

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