Question

Assume the diameter of tennis balls (under standard conditions) is normally distributed, with a mean diameter of 6.7cm and a standard deviation of 0.12cm If the random variable described here is represented as X, then identify its type of distribution and write down the value(s) of its parameters then Calculate the probability using statistical tables that a randomly selected ball has a diameter less than 6.52cm.

Answer 1

The random variable X is normally distributed (bell shaped or mound shaped) with parameters mean, = 6.7 cm and standard deviation, = 0.12 cm

P(X < A) = P(Z < (A - )/)

The probability value corresponding to an Z score can be obtained from the standard normal distribution table.

P(a randomly selected ball has a diameter less than 6.52) = P(X < 6.52)

= P(Z < (A - (6.52 - 6.7)/0.12)

= P(Z < -1.5)

= 0.0668