Question 1

Paper 1, no calculatorMedium8 marks

A machine produces metal pins whose lengths are modelled by a normal distribution with mean 4242 mm and standard deviation 33 mm.

For this question, use the facts that approximately 68%68\% 95%95\% and 99.7%99.7\% of values lie within one, two and three standard deviations of the mean, respectively.

(a)

Estimate the percentage of pins with lengths between 3939 mm and 4545 mm.

[1]
(b)

Hence, estimate the percentage of pins with lengths between 3939 mm and 4848 mm.

[3]
(c)

A batch contains 800800 pins. Hence, estimate the number of pins in the batch with lengths between 3939 mm and 4848 mm.

[2]
(d)

A pin has length 5151 mm. Estimate the percentage of pins with lengths greater than 5151 mm, giving your reasoning.

[2]

More AA 4.4 Probability distributions questions