See attached and solve c) substituting 142 businesses for the 150 on the original ### 8.32 PLANNING A SURVEYYou are planning a sample survey of small businesses in your area. You will choose a Simple Random Sample (SRS) of businesses listed in the telephone book’s Yellow Pages. Experience shows that only about half the businesses you contact will respond.#### (a) If you contact 150 businesses, it is reasonable to use the binomial distribution with \(n = 150\) and \(p = 0.5\) for the number \(X\) who respond. Explain why.- **B**: Only two choices, respond or not - **I**: It is reasonable to believe that all responses are independent - **N**: \(n = 150\) - **S**: All have the same probability of success (response) \(= 0.5\) #### (b) What is the expected number (the mean) who will respond?\[\mu = 150(0.5) = 75 \text{ responses}\]#### (c) What is the probability that 70 or fewer will respond? (Use the normal approximation.)\[\sigma = \sqrt{npq} = \sqrt{150(0.5)(0.5)} = 6.1237\]\[P(X \leq 70) = P \left( Z \leq \frac{70 - 75}{6.1237} \right) = P(Z \leq -0.82) = 0.2071\]#### (d) How large a sample must you take to increase the mean number of respondents to 100?You must increase the sample to 200, since \(200(0.5) = 100\).

Name: See attached and solve c) substituting 142 businesses for the 150 on t
Uploaded: 2024-03-20T07:06:41.000Z
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Description: See attached and solve c) substituting 142 businesses for the 150 on the original ### 8.32 PLANNING A SURVEYYou are planning a sample survey of small businesses in your area. You will choose a Simple Random Sample (SRS) of businesses listed in the te