Question

The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110. What is the probability that a randomly selected student has a score between 350 and 550? Use the portion of the standard normal table below to help answer the question. z Probability 0.00 0.5000 0.25 0.5987 0.35 0.6368 0.45 0.6736 1.00 0.8413 1.26 0.8961 1.35 0.9115 1.36 0.9131

Answer 1

59%................................................................

Answer 2

Μ = 500, population mean
σ = 110, population stadard deviation

The given table is
z  0.00       0.25       0.35      0.45      1.00      1.26       1.35     1.36
P  0.5000  0.5987  0.6368  0.6736  0.8413  0.8961  0.9115  0.9131

Range of random variable is X = [350, 550].

Calculate z-score for x = 350.
z = (350 - 500)/110 = -1.364
From the given tables,
The probability at x = 350 is
1 - 9131 = 0.0869

Calculate the z-score for x = 550.
z = (550 - 500)/110 = 0.454
From the given tables,
The probability at x = 550 is 0.6736

The probability that x =[350,550] is 
0.6736 - 0.0869 = 0.5867

Answer:  0.5867  (or 58.7%)