Not sure how to go about this problem or get it started. Which type of analysis method should I use?

Background John Draper is a field geologist working for the National Oil Company. John works with a small group of highly trained people who, quite literally, walk the Earth looking for new sources of oil. In their search for oil that may be many thousands of feet below the earth's surface, the team makes use of highly sophisticated electronic equipment. In preparation for an upcoming trip to search for oil in the Australian Outback, the team has been working on some new equipment that will be used. John is especially concerned with a problem he is having with a particular component part on the new equipment. Problem Details The equipment specifications called for 200 of the components, with each having a diameter of between 0.15 inch and 0.18 inch. The supplier identified to supply the component states that they manufacture the part to specifications calling for Normally distributed output, with a mean of 0.16 inch and a standard deviation of 0.02 inch. John must be prepared to report Monday morning on two issues of concern:

1. Does the supplier actually produce parts according to their stated specifications? 2. If, and only if, the parts are made to specifications, how many components must be purchased in order to have enough acceptable components to make two oil exploration devices? If the evidence refutes the supplier's claim, John will recommend that a search for a new supplier begin immediately.

The supplier has provided the data in the following table representing measurements from a random sample of 330 components.

Diameter (Inch) Frequency < 0.14 5 0.14 to < 0.15 70 0.15 to < 0.16 90 0.16 to < 0.17 105 0.17 to < 0.18 50 > 0.18 10