Consider a random sample of size n = 31, with sample mean \bar{x}=45.2 and sample standard deviation s = 5.3. Compute 90%, 95%, and 99% confidence int

A palindromic number is a natural number whose reversal is identical to itself. For instance, the numbers: 1, 99, 101, 2112, 44444 are respectively palindromic numbers of 1, 2, 3, 4, and 5 digits. How many palindromic numbers between 1000 and 1000 000 are there?

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Brittany Patton

A palindromic number is a natural number whose reversal is identical to itself. We need to find the total number of palindromic numbers between 1000 and 1000000.
Now, since 1000000 is itself not a palindromic, so we consider only integers till only 6 digits. Therefore, we need to find the palindromic number of digits 4,5 and 6.
First, we find the palindrome of 4 digit. The type of 4 digit palindrome can be written as: a00a,a11a,a22a,...,a99a
So there are 9 possibilities of each a. Therefore, there are $$9\times10=90$$ palindrome of digit 4.
Next, we find the 5 digit palindromes. The form of 5 digit palindrome are ab0ba,ab1ba,ab2ba,...,ab9ba
There are 9 possibilities for each a and 10 possibilities for each b. Thus, the total number of palindromes of digit 5 are $$9\times10\times10=900.$$
Finally, the type of the 6 digit palindromes are given as: ab00ba,ab11ba,ab22ba,...,ab99ba
There are 9 possibilities for each a and 10 possibilities for each b. Thusm the total number of palindromes of digit 6 are $$9\times10\times10=900$$
Thus, the total number of palindromic numbers between 1000 and 1000000 are $$90+900+900=1890.$$

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