Question

I would prefer to use technology over tables if possible- please show me how/what to enter into Excel. Thank you!!

1. A) The combined SAT scores for the students at a local high school are normally distributed with a mean of 1507 and a standard deviation of 296. The local college includes a minimum score of 1773 in its admission requirements.
What percentage of students from this school earn scores that fail to satisfy the admission requirement? (Where on the table do I find this Value??)

B) The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 63 and a standard deviation of 8. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 55 and 63?

C) Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested.
If 4.7% of the thermometers are rejected because they have readings that are too high and another 4.7% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others.

Answer 1

a) P(X < 1773)

= P((X - )/ < (1773 - )/)

= P(Z < (1773 - 1507)/296)

= P(Z < 0.90)

= 0.8159 = 81.59%

b) 63 - 8 = 55

According to the empirical rule about 68% of the data fall within 1 standard deviation from the mean.

So 34% of the data will fall within the mean and below 1 standard deviation from the mean.

So 34% of lightbulbs replacement requests numbering between 55 and 63.

C) P(X > x) = 0.047

or, P((X - )/ > (x - )/) = 0.047

or, P(Z > (x - 0)/1) = 0.047

or, P(Z < x) = 0.953

or, x = 1.675

P(X < x) = 0.047

or, P((X - )/ < (x - )/) = 0.047

or, P(Z < (x - 0)/1) = 0.047

or, P(Z < x) = 0.047

or, x = -1.675

So the two cutoff values are -1.675 and 1.675