The mean weight of a 2-year ol
The mean weight of a 2-year old is 27.5 pounds with a standarddeviation of 2.3 pounds, although some 2-year olds weigh as much as39 pounds. A health official randomly selects the medical recordsof 50 2-year olds to study. What is the probability the mean weightof the health official’s sample is more than 28.5 pounds? A) 0.001 B) 0.332 C) 0.668 D) 0.999 E) This cannot be determinedbecause the distribution is skewed right due to the 2-year oldsthat weigh as much as 39 pounds.
Answer:
= 27.5pounds
= 2.3pounds’
n = 50
Since the sample is sufficiently large (>30), we can expectthe sampling distribution of mean to be approximately normal.
P(
< A) = P(Z < (A – 
)/
)
= = 27.5pounds
= 
= 2.3/
50
= 0.3253
P(mean weight of the health official’s sample is more than 28.5pounds) = P(> 28.5)
= 1 – P(< 28.5)
= 1 – P(Z < (28.5 – 27.5)/0.3253)
= 1 – P(Z < 3.07)
= 1 – 0.9989
= 0.001 (option A)
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