Growing plants in a greenhouse can be a gardener's dream come true. However, you need to know how to maintain optimum conditions in your greenhouse if you want your plants to thrive. While each plant is different, the ideal greenhouse temperature for most plants and vegetables is normally distributed with a mean of $27\mathrm{.}06$ degrees Celsius and a standard deviation of $0\mathrm{.}94$ degrees.

Draw diagrams to help you solve the following problems

$(1$ mark$)$ What is the probability that the temperature is $26\mathrm{.}27$ degrees Celsius or lower on a randomly selected day? $(3$dp$)$

$(2$ mark$)$ In general, the range that will keep most plants alive and healthy is $29\mathrm{.}69$ and $25\mathrm{.}35$ degrees Celsius. What is the probability that the temperature falls between this ideal range? $(3$dp$)$

$(1$ mark$)$ On a randomly selected day, the temperature rises to $31\mathrm{.}5$ degrees Celsius. Do you thir it is unusual and concerning?

$(2$ mark$)$ Determine the temperature which is on the $30$th percentile of this distribution?

$(2$dp$)$