Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.23cm and a standard deviation of 0.35cm. Using the empirical rule, what percentage of the apples have diameters that are no more than 6.18cm? Please do not round your answer.

0.15% of the apples have diameters that are no more than 6.18cm.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 7.23, standard deviation = 0.35.

What percentage of the apples have diameters that are no more than 6.18cm?

6.18 = 7.23 - 3*0.35

So 6.18cm is three standard deviations below the mean.

99.7% of the measures are within 3 standard deviations of the mean. The normal distribution is symmetric, which means that (100-99.7)/2 = 0.15% is 3 standard deviations or more below the mean, and 0.15% is 3 standard deviations or more above the mean.

Thus, 0.15% of the apples have diameters that are no more than 6.18cm.

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step-by-step explanation:

answers

\3. yes the presentation (i.e. odd numbers being written as differences of two squares) is possible for all odd natural number however the presentation may not be unique. for example,  57=112−82=292−28257=112−82=292−282.

\4. 2 can't be written as a difference of two squares because 4-1=3 and 1-1=0 and the difference of squares grows to integers larger that 3.

can i get some in proving questions 1 and 2?