Question

Free range eggs are produced on a farm. The weights of eggs are found to be normally distributed with a mean of 55g and a standard deviation of 1g. Using the empirical rule and no calculations, determine whether it is likely a randomly chosen egg from the farm would have the following weight.



a. 51g
b. 53g
c. 56g

Answer 1

Answer on Question #69902 – Math – Statistics and Probability

Question

Free range eggs are produced on a farm. The weights of eggs are found to be normally distributed with a mean of 55g and a standard deviation of 1g. Using the empirical rule and no calculations, determine whether it is likely a randomly chosen egg from the farm would have the following weight.

a. 51g

b. 53g

c. 56g

Solution

By the empirical rule,

$$\begin{array}{l} P(\mu - \sigma < X < \mu + \sigma) = 0.68, \\ P(\mu - 2\sigma < X < \mu + 2\sigma) = 0.95, \\ P(\mu - 3\sigma < X < \mu + 3\sigma) = 0.997. \end{array}$$

So

a. $P(X < 51) = P(X < \mu - 4\sigma) < P(X < \mu - 3\sigma) < \frac{1 - 0.997}{2} = 0.0015$ – very unlikely.

b. $P(X < 53) = P(X < \mu - 2\sigma) = \frac{1 - 0.95}{2} = 0.025$ – unlikely.

c. $P(X > 56) = P(X > \mu + \sigma) = \frac{1 - 0.68}{2} = 0.16$ – not unlikely.

Answer: a. very unlikely; b. unlikely; c. not unlikely.

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