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Answer :
To determine the smallest sample size that satisfies the large count condition, we use the condition that both [tex]\( n \times p \)[/tex] and [tex]\( n \times (1 - p) \)[/tex] should be greater than or equal to 10. Here, [tex]\( p \)[/tex] is given as 0.55.
Let's calculate:
1. For [tex]\( n \times p \geq 10 \)[/tex]:
[tex]\[
n \times 0.55 \geq 10
\][/tex]
Simplifying this, we find:
[tex]\[
n \geq \frac{10}{0.55} \approx 18.18
\][/tex]
2. For [tex]\( n \times (1 - p) \geq 10 \)[/tex]:
[tex]\[
n \times 0.45 \geq 10
\][/tex]
Simplifying this, we find:
[tex]\[
n \geq \frac{10}{0.45} \approx 22.22
\][/tex]
Since both conditions must be satisfied, we take the larger value of [tex]\( n \)[/tex] from the two calculations. Therefore, we need:
[tex]\[
n \geq 22.22
\][/tex]
Hence, the smallest whole number that satisfies this condition is 23. Thus, the smallest sample size from the given options that satisfies the large count condition is 23.
Therefore, the answer is b. 23.
Let's calculate:
1. For [tex]\( n \times p \geq 10 \)[/tex]:
[tex]\[
n \times 0.55 \geq 10
\][/tex]
Simplifying this, we find:
[tex]\[
n \geq \frac{10}{0.55} \approx 18.18
\][/tex]
2. For [tex]\( n \times (1 - p) \geq 10 \)[/tex]:
[tex]\[
n \times 0.45 \geq 10
\][/tex]
Simplifying this, we find:
[tex]\[
n \geq \frac{10}{0.45} \approx 22.22
\][/tex]
Since both conditions must be satisfied, we take the larger value of [tex]\( n \)[/tex] from the two calculations. Therefore, we need:
[tex]\[
n \geq 22.22
\][/tex]
Hence, the smallest whole number that satisfies this condition is 23. Thus, the smallest sample size from the given options that satisfies the large count condition is 23.
Therefore, the answer is b. 23.
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