Question

A.) Let XX represent the full height of a certain species of tree. Assume that XX has a normal probability distribution with a mean of 114.5 ft and a standard deviation of 7.8 ft.
A tree of this type grows in my backyard, and it stands 98.1 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.
P(X<98.1)P(X<98.1) =
My neighbor also has a tree of this type growing in her backyard, but hers stands 137.9 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers.
P(X>137.9)P(X>137.9) =
Enter your answers as decimals accurate to 4 decimal places.

B.) Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested.
If 0.5% of the thermometers are rejected because they have readings that are too high and another 0.5% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others. Round answers to 3 decimal places.
interval of acceptable thermometer readings =

C.) Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P₉₄, the 94-percentile. This is the temperature reading separating the bottom 94% from the top 6%.
P₉₄ =

D.) Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -0.847°C and 0°C.
P(−0.847<Z<0)=

Answer 1