5. Rosie keeps bees. The amount of honey, in kg, produced by a hive of Rosie's bees in a season, is modelled by a normal distribution with a mean of 22 kg and a standard deviation of 10 kg .
- Find the probability that a hive of Rosie's bees produces less than 18 kg of honey in a season.
The local bee keepers’ club awards a certificate to every hive that produces more than 39 kg of honey in a season, and a medal to every hive that produces more than 50 kg in a season. Given that one of Rosie's bee hives is awarded a certificate
- find the probability that this hive is also awarded a medal.
(5)
Sam also keeps bees. The amount of honey, in kg, produced by a hive of Sam's bees in a season, is modelled by a normal distribution with mean \(\mu \mathrm { kg }\) and standard deviation \(\sigma \mathrm { kg }\). The probability that a hive of Sam’s bees produces less than 28 kg of honey in a season is 0.8413
Only 20\% of Sam's bee hives produce less than 18 kg of honey in a season. - Find the value of \(\mu\) and the value of \(\sigma\). Give your answers to 2 decimal places.
(6)
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