Question

If grades on an examination are approximately normally distributed, with an average of 70 and a standard deviation of 10, what is the probability that students: Received grades higher than 85? - -> P(X> 85) =? _____ (x.xxxx)

Answer 1

To find the probability of students receiving grades higher than 85, we can standardize the value and use a z-table or calculator.

Step-by-step explanation:

To find the probability that students received grades higher than 85, we need to calculate the area under the normal distribution curve to the right of 85. The mean of the distribution is 70 and the standard deviation is 10. We can standardize the value of 85 using the formula z = (x - mean) / standard deviation.

Plugging in the values, we get z = (85 - 70) / 10 = 1.5. To find the probability, we look up the z-score in the z-table or use technology.

P(X > 85) = P(Z > 1.5) = 1 - P(Z < 1.5). Using the z-table or a calculator, we find P(Z < 1.5) = 0.9332. Therefore, P(X > 85) = 1 - 0.9332 = 0.0668, or approximately 0.07.