A science experiment calls for mixing 3 and two-thirds cups of distilled water with 1 and three-fourths cups of vinegar and Two-
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Answer:
The probability that all 70 messages are transmitted in less than 12 minutes is 0.117.
Step-by-step explanation:
Let <em>X</em> = the transmission time of each message.
The random variable <em>X</em> follows an Exponential distribution with parameter <em>λ</em> = 5 minutes.
The expected value of <em>X</em> is:
The variance of <em>X</em> is:
Now define a random variable <em>T</em> as:
T = X₁ + X₂ + ... + X₇₀
According to a Central limit theorem if a large sample (<em>n</em> > 30) is selected from a population with mean μ and variance σ² then the sum of random variables <em>X</em> follows a Normal distribution with mean, and variance,
.
Compute the probability of T < 12 as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that all 70 messages are transmitted in less than 12 minutes is 0.117.