1.After 1964, quarters were manufactured so that the weights had a mean of 5.67g and a standard deviation of 0.06g. Some vending machines are designed so that you can adjust the weights of quarters that are accepted. If any counterfeit coins are found, you can narrow the range of acceptable weights with the effect that most counterfeit coins are rejected along with some with some legitimate quarters.( a ) If you adjust vending machines to accept weights between 5.64g and 5.70g, what percentage of legal quarters is rejected ?( b ) If you adjust vending machines to accept all legal quarters except those with weights in the top 2.5% and the bottom 2.5%, what are the limits of the weights that are accepted?2. Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. ( a ) Find the probability that a randomly selected adult has an IQ in between 80 and 120.( b ) If 10 adults are randomly selected, find the probability that they have mean IQ of 120.
3. Birth weights in the US are normally distributed with a mean of 3420g and a standard