Questions: According to mashable.com, 37% of Snapchat users use the app for Creativity. A random sample of 28 users was selected. Assuming this estimate is true, use the normal approximation to the binomial distribution to complete parts a through e. a. Calculate the mean and standard deviation for this distribution. Let a success be a Snapchat user that uses the app for Creativity. The mean is 10.36. (Type an integer or a decimal. Do not round.) The standard deviation is 2.555. (Round to three decimal places as needed.) b. What is the probability that 12 or more of the 28 users use the app for Creativity? The probability is . (Round to four decimal places as needed.)

Solution Steps

For a binomial distribution, the mean \( \mu \) and standard deviation \( \sigma \) can be calculated using the formulas:

\[ \mu = n \cdot p = 28 \cdot 0.37 = 10.36 \]

\[ \sigma = \sqrt{n \cdot p \cdot q} = \sqrt{28 \cdot 0.37 \cdot (1 - 0.37)} = \sqrt{6.527} \approx 2.555 \]

Thus, we have:

• Mean: \( \mu = 10.36 \)
• Standard Deviation: \( \sigma \approx 2.555 \)

To find the probability that 12 or more users use the app for Creativity, we first calculate the z-score for \( X = 12 \) using continuity correction:

\[ z = \frac{X - \mu}{\sigma} = \frac{11.5 - 10.36}{2.555} \approx 0.4462 \]

Using the z-score, we can find the probability \( P(X \geq 12) \):

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(\infty) - \Phi(0.4462) \]

From standard normal distribution tables or calculators, we find:

\[ \Phi(0.4462) \approx 0.3277 \]

Thus, the probability that 12 or more users use the app for Creativity is:

\[ P(X \geq 12) \approx 1 - 0.3277 = 0.6723 \]

Final Answer