"Nails Ur Way" is a large manufacturer of various kinds of liquid nail polish. The quality control department has noted that the bottles of polish marked 4 ounces vary in content with a standard deviation of 0.25 ounces. Assume the contents of the bottles are normally distributed. a. What percentage of all bottles produced contains more than 4.51 ounces of vitamins? b. What percentage of all bottles produced contains less than 4.925 ounces? c. What percentage of bottles produced contains between 3.6 to 4.2 ounces? d. Ninety-five percent of the bottles will contain at least how many ounces? e. What percentage of the bottles contains between 4.3 and 4.6 ounces?

The weights for newborn babies is approximately normally distributed with a mean of 6.5 pounds and a standard deviation of 1.3 pounds.Consider a group of 1400 newborn babies:1. How many would you expect to weigh between 3 and 8 pounds? 2. How many would you expect to weigh less than 6 pounds? 3. How many would you expect to weigh more than 4 pounds? 4. How many would you expect to weigh between 6.5 and 10 pounds?

Sarah and her fiancé are planning for their wedding. Distribution of the number of guests coming to the party is normal with the mean 100 and the standard deviation 10. They need to determine how many guests to book for food from a caterer. The caterer makes the following charges: $50 for each guest that is booked in advance; $90 for each guest who is not booked in advance but shows up on the wedding day. The caterer does not offer any refund even if some booked guests may not show up.                                                         Questions: What is the optimal number of guests to book in advance? How much Sarah can save by booking the optimal quantity from a) in advance? What is the expected number of guests that will come to their wedding? If Sarah and her fiancé book 90 guests in advance with the caterer, what is the probability of stock out? If Sarah and her fiancé book 100 guests in advance with the caterer, what is the expected number of meals to be wasted?

According to a government study among adults in the 25 to 34-year age group, the mean amount spent per year on reading and entertainment is $1,994.  Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $350. a.   What percent of the adults spend more than $2,500 per year on reading and entertainment? b.   What percent spend between $2,500 and $2,800 per year on reading and entertainment?