Question 1 (a) Manufactured articles are packed in boxes each containing 200 articles, and on average 1.5% of all articles manufactured are defective. A box which contains 4 or more defective articles is said to be substandard. (i) Using a suitable approximation, show that the probability that a randomly chosen box will be substandard is 0.353, correct to 3 decimal places. A lorry-load consists of 16 boxes, randomly chosen. (ii) Find the probability that a lorry-load will contain at most 2 boxes which are substandard, giving three decimal places in your answer A warehouse holds 100 lorry-loads. (iii) Show that, correct to two decimal places, the probability that exactly one of the lorry-loads in the warehouse will include at most 2 substandard boxes is 0.06. (b) The volumes of wine in bottles are normally distributed with a mean of 760 ml and standard deviation of 12 ml. (i) Find the probability that a bottle of wine picked at random from this distribution contains more than 769 ml. (ii) A wine merchant orders 800 bottles of wine. Estimate the number of bottles containing less than 750 ml
Question 1
(a) Manufactured articles are packed in boxes each containing 200 articles, and on average
1.5% of all articles manufactured are defective. A box which contains 4 or more
defective articles is said to be substandard.
(i) Using a suitable approximation, show that the
box will be substandard is 0.353, correct to 3 decimal places.
A lorry-load consists of 16 boxes, randomly chosen.
(ii) Find the probability that a lorry-load will contain at most 2 boxes which are
substandard, giving three decimal places in your answer
A warehouse holds 100 lorry-loads.
(iii) Show that, correct to two decimal places, the probability that exactly one of the
lorry-loads in the warehouse will include at most 2 substandard boxes is 0.06.
(b) The volumes of wine in bottles are
standard deviation of 12 ml.
(i) Find the probability that a bottle of wine picked at random from this distribution
contains more than 769 ml.
(ii) A wine merchant orders 800 bottles of wine. Estimate the number of bottles
containing less than 750 ml
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