At the end of section 8.3 it was noted that the samples of serum cholesterol lev

Question

At the end of section 8.3 it was noted that the samples of serum cholesterol levels of size 2.5- drawn from a population with mean =211 mg/100 ml and standard deviation = 46 mg/100 ml- the probability that a sample mean X lies within the interval (193.0, 229.0) is .95. Furthermore, the probability that the mean lies below 22.6 mg/100ml is .95, and the probability that is it above 195.9 mg/100ml is .95. For all three of these events to happen simultaneously, the sample mean X would have to lie in the interval (195.9, and 226.1) What is the probability that this occurs?

Explanation / Answer

  probability that sample mean X would have to lie in the interval (195.9, and 226.1):

for normal distribution z score =(X-)/ here mean=       = 211 std deviation   == 46.0000 sample size       =n= 25 std error=x=/n= 9.2000

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