Question

A haulage firm has 24 lorries, 15 of these are articulated

i) What is the probability that 3 randomly selected lorries are articulated ?

ii) what is the probability that no articulated lorries would be chosen if 4 lorries were randomly selected?

iii) what is the probability that more than 3 articulated lorries would be chosen if 6 were randomly selected?

Q) If holes drilled in a metal plate have a normal distribution with a mean diameter of 16.4mm and a standard deviation of 0.8mm, and a set of bolts have a normal distribution with a mean diameter of 16mm and a standard deviation of 0.5mm, what is the probability of randomly selected bolt fitting a randomly selected hole?

Answer 1

i)

Probability that 3 randomly selected lorries are articulated

= = 0.2248

ii) Probability that no articulated lorries would be chosen if 4 lorries were randomly selected

= = 0.0119

iii) The probability that more than 3 articulated lorries would be chosen if 6 were randomly selected

=

= 0.6031

Q)

For hole in metal plate:

Mean, = 16.4 mm

Standard deviation, = 0.8 mm

For bolt:

Mean = 16 mm

Standard deviation = 0.5 mm

A bolt fits a hole if the hole is of larger or of the same size as a bolt

The distribution of the difference in size of hole and bolt D has mean = 16.4 - 16 = 0.4

and Standard deviation = = 0.9434

The probability of randomly selected bolt fitting a randomly selected hole = P(d ≥ 0)

= P{Z ≥ (0 - 0.4)/0.9434}

= P(Z ≥ -0.424)

= 0.6642