Question

how many pets do you think a family should have?

a poll asked 1006 random adults.

49% said 2 animals is good.

suppost p=.49 (exactly true for the population of adults).

a) explain why X is a binomial random variable

b) find the mean and standard dev of x

c) find probability X=493

d) use normal approx to find P(number of adults who thought 2 animals were fine is between 461/525)

please show work neatly!

X = number of adults who thought 2 animals were fine

Answer 1

a) This is a binomial distribution question with

n = 1006

p = 0.49

q = 1 - p = 0.51

where

b)

Since we know that

d)

\\z_{ score } = \frac{x-\mu}{\sigma}

P(461.0 < x < 525.0)=?

This implies that

P(461.0 < x < 525.0) = P(-2.0144 < z < 2.022) = 0.9564

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