The number of standard deviations a particular X value is from the mean is commo
ID: 3319067 • Letter: T
Question
The number of standard deviations a particular X value is from the mean is commonly referred to as ________.
Assume that men's weights are normally distributed with a mean of 170 lb and standard deviation of 27 lb (National Health Survey) If 45 men are randomly selected, find the probability that they have a mean weight less than 167 lb.
The average teacher's salary in X-state is $30,450. Assume a normal distribution with = $4,500. What is the probability that the mean for a sample of 70 teacher's salaries is greater than $31,000?
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Explanation / Answer
The number of standard deviations a particular X value is from the mean is commonly referred to as z -value.
A) P(x < 167)
= P((x - mean)/(SD/sqrt(n)) < (167 - mean)/(SD /sqrt(n))
= P(Z < (167 - 170)/(27/sqrt(45))
= P(Z < -0.75)
= 0.2266
B) P(X > 31000) = P((x - mean)/(SD/sqrt(n)) > (31000 - mean)/(SD /sqrt(n))
= P(Z > (31000 - 30450)/(4500/sqrt (70))
= P(Z > 1.02)
= 1 - P(Z < 1.02)
= 1 - 0.8461
= 0.1539