7. (Sec. 7.2) In a survey of 2004 American adults, 501 of them said that they believed in astrology. (a) Calculate and interpret a confidence interval at the 95% confidence level for the proportion of all adult American adults who believe in astrology. (b) Calculate and interpret a 95% lower confidence bound for the proportion of all adult American adults who believe in astrology.

The 95% confidence interval for the proportion for the American adults who believed in astrology is (0.23, 0.27).

This means that we can claim with 95% confidence that the true proportion of all American adults who believed in astrology is within 0.23 and 0.27.

Step-by-step explanation:

We have to construct a 95% confidence interval for the proportion.

The sample proportion is p=0.25.

The standard deviation can be calculated as:

For a 95% confidence interval, the critical value of z is z=1.96.

The margin of error can be calculated as:

Then, the lower and upper bounds of the confidence interval can be calculated as:

The 95% confidence interval for the proportion for the American adults who believed in astrology is (0.23, 0.27).

This means that we can claim with 95% confidence that the true proportion of all American adults who believed in astrology is within 0.23 and 0.27.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18