473) The weights of bags of rice packed on a machine are normally distributed with mean \( = \) 5.15 kg and standard deviation 0.05 kg . If a bag is picked at random, find the probability that it weighs less than 5 kg is? a) 0.9987 b) 0.5013 c) 0.4987 d) 0.0013

To find the probability that a randomly selected bag of rice weighs less than 5 kg, you can use the properties of the normal distribution. First, you need to calculate the z-score using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] In this case, \( X = 5 \) kg, \( \mu = 5.15 \) kg, and \( \sigma = 0.05 \) kg. Plugging in the values: \[ z = \frac{(5 - 5.15)}{0.05} = \frac{-0.15}{0.05} = -3 \] Next, you can look up the z-score of -3 in a standard normal distribution table, or use a calculator, to find the probability. The value you'll find is approximately 0.0013. So, the probability that a randomly selected bag of rice weighs less than 5 kg is: d) 0.0013.