The weights, in grams, of individual packets of coffee can be modelled by a normal distribution, with mean 102g and standard deviation 8g. a) Find the probability that a randomly selected packet has a weight less than 100g. b) The probability that a randomly selected packet has a weight greater than w gramsi 0.444. Find the value of w. c) A packet is randomly selected. Given that the packet has a weight greater than 105g , find the probability that it has a weight greater than 110g.

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The weights, in grams, of individual packets of coffee can be modelled by a normal
distribution, with mean 102g and standard deviation 8g.
a) Find the probability that a randomly selected packet has a weight less than 100g.
b) The probability that a randomly selected packet has a weight greater than w grams
0.444. Find the value of w.
c) A packet is randomly selected. Given that the packet has a weight greater than 105g
find the probability that it has a weight greater than 110g .
d) From a random sample of 500 packets, determine the number of packets that would
be expected to have a weight lying within 1.5 standard deviations of the mean.
e) Packets are delivered to supermarkets in batches of 80. Determine the probability the
least 20 packets from a randomly selected batch have a weight less than 95g.
Transcribed Image Text:The weights, in grams, of individual packets of coffee can be modelled by a normal distribution, with mean 102g and standard deviation 8g. a) Find the probability that a randomly selected packet has a weight less than 100g. b) The probability that a randomly selected packet has a weight greater than w grams 0.444. Find the value of w. c) A packet is randomly selected. Given that the packet has a weight greater than 105g find the probability that it has a weight greater than 110g . d) From a random sample of 500 packets, determine the number of packets that would be expected to have a weight lying within 1.5 standard deviations of the mean. e) Packets are delivered to supermarkets in batches of 80. Determine the probability the least 20 packets from a randomly selected batch have a weight less than 95g.
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