Assume a random sample representative of the population is surveyed. If 20 people in the sample of size 54 are in favor, can the normal distribution approximation be used to estimate probabilities? (a) $$ n p= $$ (b) $$ n(1-p)= $$ (c) Yes, a normal distribution approximation can be used No, a normal distribution approximation can't be used

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**Step 1: Calculate $$ n p $$**

Given that the sample size is $$ n = 54 $$ and the number in favor is 20, the sample proportion is  
$$
p = \frac{20}{54}.
$$
Then,  
$$
n p = 54 \times \frac{20}{54} = 20.
$$

**Step 2: Calculate $$ n(1-p) $$**

Since  
$$
1-p = 1 - \frac{20}{54} = \frac{34}{54},
$$
we have  
$$
n(1-p)= 54 \times \frac{34}{54} = 34.
$$

**Step 3: Check if the normal approximation can be used**

A common rule of thumb for using the normal approximation is that both $$ n p $$ and $$ n(1-p) $$ should be at least 10. Here,  
$$
n p = 20 \quad \text{and} \quad n(1-p) = 34,
$$
which both satisfy the criterion.

**Answers:**  
(a) $$ n p = 20 $$  
(b) $$ n(1-p) = 34 $$  
(c) Yes, a normal distribution approximation can be used.
(a) $$ n p = 20 $$ (b) $$ n(1-p) = 34 $$ (c) Yes, a normal distribution approximation can be used

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