normally distributed score have mean 100 and standard deviation 15. use the standard z-table to the following; probability of randomly selecting someone with score less than 80, greater than 136 and between 95 and 110

To answer this question, we need to convert the scores to z-scores and then use the standard z-table to find the probabilities.

1. Probability of randomly selecting someone with a score less than 80:

   Z = (X - μ) / σ = (80 - 100) / 15 = -1.33

   Looking up this z-score in the z-table, we find a probability of 0.0918. So, the probability of randomly selecting someone with a score less than 80 is 0.0918 or 9.18%.

2. Probability of randomly selecting someone with a score greater than 136:

   Z = (X - μ) / σ = (136 - 100) / 15 = 2.4

   Looking up this z-score in the z-table, we find a probability of 0.9918. However, since we want the probability of a score greater than 136, we need to subtract this value from 1. So, the probability is 1 - 0.9918 = 0.0082 or 0.82%.

3. Probability of randomly selecting someone with a score between 95 and 110:

   For X = 95, Z = (95 - 100) / 15 = -0.33. The corresponding probability from the z-table is 0.3707.

   For X = 110, Z = (110 - 100) / 15 = 0.67. The corresponding probability from the z-table is 0.7486.

   To find the probability of a score between 95 and 110, subtract the smaller probability from the larger one: 0.7486 - 0.3707 = 0.3779 or 37.79%.