The median score is 76. We do not know the standard deviation exactly, but a typical distance from the mean must be larger than four if the quartiles are so spread. The distribution of volumes of soda in cans is normal with a mean of 12.2 ounces and a standard deviation of 0.1 ounces. The median of the distribution is 12.2 ounces. 12 ounces is two stsandard deviations below the mean.
Normal curves are symmetric about the mean.
Half of these will be below the mean. The CLT tells us the sampling distribution of the sample mean in this problem will be normal with a mean of 12.2 ounces and SE 0.02. The probability is 0.09375. A student takes a random sample of 50 beads. Write an expression for the exact probability that 20 or more sampled beads are red.