1. About as many boys as girls are born in hospitals. Many babies are born every week in the large city of Manchester. In Cornwall, a country town, there is a small hospital where only a few babies are born every week. A normal week is one in which between 45% and 55% of the babies are female. An unusual week is one in which more than 55% are girls or more than 55% are boys.

1. How does the notion of stability, or stable relative frequencies, explain why it is more unlikely for there to be an unusual week in Manchester than in Cornwall? (2 pts.)

2. Six students took a standardized exam. Their scores (out of 100) are as follows: 45, 74, 98, 63, 87, 59.

a) What is their sample mean score? (1 pt.) b) What is their sample median score? (1 pt.)

3. Suppose that only of the iPads from Apple's Chinese production line last past the length of the warranty. Assume that the production of iPads is a sort of Bernoulli trial with a constant probability and independent results.

a) What is the expected number of iPads that outlast the warranty in a production batch of 4800? (1 pt.)

b) What is the theoretical standard deviation? (1 pt.)

c) How probable it is, based on the degree of variance from the mean, that the number of long-lasting iPads in this batch will lie between 3510 and 3690? Express your answer in terms of a percentage. (1 pt.)

4. Suppose that you are a regional manager for a popular surf shop here in Oahu and are responsible for ordering office supplies, say light bulbs for all of your stores. Of those that get delivered, 15% arrive defective (are either broken or do not work), while 85% are unbroken. Given shipping costs, the smallest production run is 1,000 lightbulbs. You order 5,000 lightbulbs for your 5 stores (i.e., 1,000 for each).

a) What is the theoretical mean (i.e., the expected number of unbroken lightbulbs in the shipment)? (1 pt.)

b) What is the theoretical standard deviation? (1 pt.)

c) What standard of deviation from the mean does this shipment of lightbulbs fall within? (1 pt.)