Question

Find the probability of selecting a score greater than negative 0.95

Find the probability of selecting a z score between negative 0.85 and 1.15 find the c-score their corresponds to p99 the 99th percentile of standard normal distribution curve find the z score that corresponds to p67 the 67th percentile of standard normal distribution curve a type of thermometer has the temperature rising at the freezing point of water that mean normally distributed with a mean of zero Celsius and a standard deviation of one Celsius and temperature corresponding to p23 the 23rd percentile find the area to the right of the piece for 2.75 under standard normal distribution curve

Answer 1

Here are the answers (standard normal, rounded to 3–4 decimal places):

1) P(Z > −0.95) = Phi(0.95) ≈ 0.8289

2) P(−0.85 < Z < 1.15) = Phi(1.15) − Phi(−0.85)
= 0.8749 − 0.1977 ≈ 0.6772

3) z for the 99th percentile (p = 0.99) ≈ 2.3263 (≈ 2.33)

4) z for the 67th percentile (p = 0.67) ≈ 0.44

5) For the thermometer (mean = 0, SD = 1): the 23rd percentile (p = 0.23) corresponds to z ≈ −0.74

6) Area to the right of z = 2.75: 1 − Phi(2.75) ≈ 0.00297

If you want more precision or the intermediate table/graph showing these, I can provide that.