The length of alike metals produced by a hardware store are approximated by a normal distribution model having a mean of 7 cm and a standard deviation of 0.35 cm Find the probability that the length of a randomly chosen metal is between 5.36 and 6.14 cm?
Answers
Given : The length of alike metals produced by a hardware store are approximated by a normal distribution model having a mean of 7 cm and a standard deviation of 0.35 cm
To find : probability that the length of a randomly chosen metal is between 5.36 and 6.14 cm
Solution:
mean = 7 cm
Standard deviation = 0.35 cm
Z score = ( Value - mean)/SD
Values 5.36 & 6.14
Z score for 5.36 = (5.36 - 7)/0.35 = -4.686 Z score - 4.686 ≈0
Z score for 6.14 = (6.14 - 7)/0.35 = -2.457 Z score -2.457 = 0.007
Probability = 0.007
probability that the length of a randomly chosen metal is between 5.36 and 6.14 cm = 0.007
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