Homework Help is Here – Start Your Trial Now!
Math
Statistics
Estimate P(6) for n = 18 and p= 0.3 by using the normal distribution as an approximation to the binomial distribution. Round to four decimal places. ..... O A. 0.1239 B. 0.1937 O C. 0.1015 O D. 0.8513

Estimate P(6) for n = 18 and p= 0.3 by using the normal distribution as an approximation to the binomial distribution. Round to four decimal places. ..... O A. 0.1239 B. 0.1937 O C. 0.1015 O D. 0.8513

icon
Related questions
Question

I was able to solve this by guessing. Please show me how to do the work and use excel if you can. Thanks!

**Problem:** Estimate \( P(6) \) for \( n = 18 \) and \( p = 0.3 \) by using the normal distribution as an approximation to the binomial distribution. Round to four decimal places. **Options:** - A. 0.1239 - **B. 0.1937** (correct answer) - C. 0.1015 - D. 0.8513 **Explanation:** To approximate a binomial probability using the normal distribution, we use the normal approximation for the binomial distribution given by: 1. Calculate the mean (\(\mu\)) and standard deviation (\(\sigma\)): - \(\mu = n \times p\) - \(\sigma = \sqrt{n \times p \times (1-p)}\) 2. Convert the binomial probability to a z-score using \( X = 6 \): - \( z = \frac{X - \mu}{\sigma} \) 3. Use the z-score to find the corresponding probability from the standard normal distribution table. The answer, rounded to four decimal places, is 0.1937, corresponding to option B.
Transcribed Image Text:**Problem:** Estimate \( P(6) \) for \( n = 18 \) and \( p = 0.3 \) by using the normal distribution as an approximation to the binomial distribution. Round to four decimal places. **Options:** - A. 0.1239 - **B. 0.1937** (correct answer) - C. 0.1015 - D. 0.8513 **Explanation:** To approximate a binomial probability using the normal distribution, we use the normal approximation for the binomial distribution given by: 1. Calculate the mean (\(\mu\)) and standard deviation (\(\sigma\)): - \(\mu = n \times p\) - \(\sigma = \sqrt{n \times p \times (1-p)}\) 2. Convert the binomial probability to a z-score using \( X = 6 \): - \( z = \frac{X - \mu}{\sigma} \) 3. Use the z-score to find the corresponding probability from the standard normal distribution table. The answer, rounded to four decimal places, is 0.1937, corresponding to option B.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer