Find mean from probability statement

1 The lengths, in metres, of cars in a city are normally distributed with mean \(\mu\) and standard deviation 0.714 . The probability that a randomly chosen car has a length more than 3.2 metres and less than \(\mu\) metres is 0.475 . Find \(\mu\).

1 The weights, in grams, of onions in a supermarket have a normal distribution with mean \(\mu\) and standard deviation 22. The probability that a randomly chosen onion weighs more than 195 grams is 0.128 . Find the value of \(\mu\).

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1. The daily minimum temperature in degrees Celsius ( \({ } ^ { \circ } \mathrm { C }\) ) in January in Ottawa is a random variable with distribution \(\mathrm { N } ( - 15.1,62.0 )\). Find the probability that a randomly chosen day in January in Ottawa has a minimum temperature above \(0 ^ { \circ } \mathrm { C }\).
2. In another city the daily minimum temperature in \({ } ^ { \circ } \mathrm { C }\) in January is a random variable with distribution \(\mathrm { N } ( \mu , 40.0 )\). In this city the probability that a randomly chosen day in January has a minimum temperature above \(0 ^ { \circ } \mathrm { C }\) is 0.8888 . Find the value of \(\mu\).

1 The random variable \(H\) has the distribution \(\mathrm { N } \left( \mu , 5 ^ { 2 } \right)\). It is given that \(\mathrm { P } ( H < 22 ) = 0.242\). Find the value of \(\mu\).