The weights of a large number of miniature poodles are approximately normally distributed with a mean of 8 kilograms and a standard deviation of 0.9 kilogram. if measurements are recorded to the nearest tenth of a kilogram, find the fraction of these poodles with weights

Using the normal distribution, it is found that:

The z-score is:

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

In this problem:

The z-score will be given by:

Applying the percentile concept:

A similar problem is given at link

b

step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.