please help thanks!!

Question

The results of an examination are found to be normally distributed with a standard deviation of 15.0. If a student is selected at random, the probability is 0.0485 that his mark will exceed 85. The mean for this test correct to the nearest tenth is?

Answer 1

σ = 15.0

 

P(X > 85) = 0.0485

1 - P(X ≤ 85) = 0.0485

P(X ≤ 85) = 0.9515

P[(X-μ)/σ ≤ (85-μ)/σ] = 0.9515

P[Z ≤ (85-μ)/15] = 0.9515

 

Using the table for normal distribution, for an area of 0.9515, we find that z ≈ 1.66. So, 

z = (85 - μ)/15 = 1.66

 

Now, solving for μ, we get μ = 85 - (15×1.66) = 60.1.

 

Thus, the mean for this test is 60.1.