NORMAL DISTRIBUTION HOMEWORK DUE TOMORROW PLEASE HELP

please help i dont understand this at all.

The incubation time for Rhode Island Red chicks is normally distributed with mean of 21 days and standard deviation of approximately 1 day. If 1000 eggs are being incubated, how many chicks do we expect will hatch

a. in 19 to 23 days?

b. in 20 to 22 days?

c. in 21 days or fewer?

d. in 18 to 24 days? (assume all eggs eventually hatch)

PLEASE HELP!!!

The incubation time for Rhode Island Red chicks is normally distributed with mean of 21 days and standard deviation of approximately 1 day. If 1000 eggs are being incubated, how many chicks do we expect will hatch

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Use \(\displaystyle z=\frac{x-{\mu}}{\sigma}\)

a. in 19 to 23 days?

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This is a case of the Empirical Rule. Or, you can use the z-table.

\(\displaystyle z=\frac{19-21}{1}=-2, \;\ z=\frac{23-21}{1}=2\)

19 days is two standard deviations below the mean, and 23 days is 2 standard deviations above the mean. One day is one standard deviation.

The Empirical Rule says that about 95% of the data falls within 2 S.D.'s of the mean. What is 95% of 1000?.

Or you could use the z-table. Look up the probability for z=-2 and z=2 in the z table. You see it is .0228 for z=-2

and .9772 for z=2. Subtract them and get .9772-.0228=.9544. This means 95.44% of the eggs will hatch between 19 and 23 days.

Very close to the 95% the Empirical Rule tells us.

Do the other problems similarly.

b. in 20 to 22 days?

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Do the same as part a except it is 1 SD above and below the mean.

c. in 21 days or fewer?

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The mean is 21 days. Half the data is higher and half less than the mean.

d. in 18 to 24 days? (assume all eggs eventually hatch)

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Do the same as part a and b.

This one again calls on the simplicity of the Empricial Rule. The mean is 21. How far is 18 from 21?. -3

How far is 24 from 21?. 3

This says that 18 days is 3 SD below the mean and 24 is 3 SD above the mean. What does the Emprirical Rule say about 3 standard deviations?.

You must be covering it now because these problems are set up around it. That is, they all work out to be integer values above and below the mean.