Question

In: Statistics and Probability

1. Suppose 30% of hoo=me owners in a country have flood insurance. Let ^p be the...

1. Suppose 30% of hoo=me owners in a country have flood insurance. Let ^p be the proportion of home with flood insurance from a random sample of 100 homes in the country.

a) Find the mean value of ^p

b) Find the standard deviation of ^p

c) how do you know that the distrobutuon of ^p is approx. normal?

d) Use normal approximation to estimate the probability of ^p < 0.25.

Expert Solution

Solution:

Given:

p = 0.30

n = 100

Part a) Find the mean value of

Part b) Find the standard deviation of :

( Round answer to specified number of decimal places)

Part c) how do you know that the distribution of is approx. normal?

Since

and

thus sampling distribution of sample proportions is approximately Normal.

Part d) Use normal approximation to estimate the probability of < 0.25.

Find z score:

thus we get:

Look in z table for z = -1.0 and 0.09 and find corresponding area.

P( Z < -1.09) = 0.1379

thus

orchestra answered 2 years ago

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