Use the central limit theorem to estimate

Reference no: EM131084283

Telephone calls can be classified as voice (V) if someone is speaking, or data (D) if there is a modem or fax transmission. Based on a lot of observations taken by the telephone company, we have the following probability model: P[V] = 0.8, P[D] = 0.2. Data calls and voice calls occur independently of one another. The random variable Kn is the number of data calls in a collection of n phone calls.

(a) What is E[K₁₀₀], the expected number of voice calls in a set of 100 calls?

(b) What is σK₁₀₀, the standard deviation of the number of voice calls in a set of 100 calls?

(c) Use the central limit theorem to estimate P[K100 ≥ 18], the probability of at least 18 voice calls in a set of 100 calls.

(d) Use the central limit theorem to estimate P[16 ≤ K₁₀₀ ≤ 24], the probability of between 16 and 24 voice calls in a set of 100 calls.

Reference no: EM131084283

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