If you select a random sample of 200 children and observe, Ask an Expert

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Let X be a discrete random variable that represents the number of diagnostic services a child receives during an office visit to a pediatric specialist; these services include procedures such as blood tests and urine-analysis. The probability distribution for X appears below:

x 0 1 2 3 4
P(X = x) 0.20 0.30 0.25 0.15 0.10

(i) If you select a random sample of 200 children and observe the number of diagnostic services each of them receives, what is the probability that the mean number of diagnostic services is more than 1.72? State clearly whether any assumption is needed and explain why.

(ii) If you select a random sample of 5 children only, what is the probability that the sample standard deviation is zero?

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