Question

Find the following percentiles for the standard normal distribution. Interpolate where appropriate.

Answer 1

To find percentiles for the standard normal distribution, use the formulas provided and the invNorm and normalcdf functions.

Step-by-step explanation:

To find the percentiles for the standard normal distribution, you can use the following formulas:

1. The 50th percentile is the mean of the distribution, which in this case is 200.
2. The 25th percentile can be found using the invNorm function with a probability of 0.25, a mean of 200, and a standard deviation of 5. This gives us a result of 196.63.
3. The 75th percentile can be found using the invNorm function with a probability of 0.75, a mean of 200, and a standard deviation of 5. This gives us a result of 203.37.
4. To find P(1.75 < x < 1.85), you can use the normalcdf function with a lower bound of 1.75, an upper bound of 1.85, a mean of 2, and a standard deviation of 0.05. This gives us a result of 0.0013.