4. A company produces steel rods whose lengths follow a normal distribution with a mean of
50 inches and a standard deviation of 2 inches.
a) What is the probability that a randomly selected steel rod has a length greater than 54
inches?
b) What is the probability that a randomly selected steel rod has a length between 48 and
52 inches?
c) If the company wants to ensure that 90% of the rods they produce have lengths within
a specific range, what should be the length range?
d) If a steel rod is randomly selected and its length is found to be 55 inches, what is the z-
score for this rod?
e) Interpret the z-score calculated in part d.
