4 questions?

Question

These are the only 4 questions I have left to answer out of 53... Please help..

1. The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30" and a sd of 0.01". In a random sample of 7 gross, approximately how many pencils would you expect to have a diameter less than 0.293"? A gross is a dozen dozen.Round your answer to the nearest whole number.

2. A certain grade egg must weigh at least 2 oz. If the weights of eggs are normally distributed with a mean of 1.5 oz and s.d. = 0.4 oz, approximately how many eggs in a random sample of 59 dozen would you expect to weigh more than 2 oz?

3. The amount of rainfall in January in a certain city is normally distributed with a mean of 3 inches and a standard deviation of 0.5 inches. Find the value of the quartile Q1.
a.3.3
b.2.7
c.2.8
d.0.8
4. Scores on a test have a mean of 89.1 and D2 is 75. The scores have a distribution that is approximately normal. Find the standard deviation.

Answer 1

Looks like you haven't become acquainted with your friendly z-chart. It is based on a "normalized" normal distriubtion with mean=1. You convert the value you are interested to a z-score of so-many positive or negative standard deviations. You can then read off the CUMULATIVE distribution from 0 to the z-score.
For example, in #1, your adjusted mean would be 1 (0.30/0.30) and the z-score would be -0.7 s.d.
The chart would tell you what the *** dist is for this value (appx 0.22), which means that 22% of a population will be less than or equal to 0.293 inch diameter. Multiply that by 7*144 for your answer.