5 The lengths, in cm, of the leaves of a particular type are modelled by the distribution \(\mathrm { N } \left( 5.2,1.5 ^ { 2 } \right)\).
- Find the probability that a randomly chosen leaf of this type has length less than 6 cm .
The lengths of the leaves of another type are also modelled by a normal distribution. A scientist measures the lengths of a random sample of 500 leaves of this type and finds that 46 are less than 3 cm long and 95 are more than 8 cm long. - Find estimates for the mean and standard deviation of the lengths of leaves of this type.
- In a random sample of 2000 leaves of this second type, how many would the scientist expect to find with lengths more than 1 standard deviation from the mean?