3. Basic Computation: Normal Approximation to a Binomial Distribution Suppose we have a binomial experiment with n = 40 trials and a probability of success p = 0.50. (a) Is it appropriate to use a normal approximation to this binomial distribu- tion? Why? (b) Compute u and or of the approximating normal distribution. (c) Use a continuity correction factor to convert the statement r≥ 23 suc- cesses to a statement about the corresponding normal variable x. (d) Estimate P(r≥ 23). (e) Interpretation Is it unusual for a binomial experiment with 40 trials and probability of success 0.50 to have 23 or more successes? Explain.
3. Basic Computation: Normal Approximation to a Binomial Distribution Suppose we have a binomial experiment with n = 40 trials and a probability of success p = 0.50. (a) Is it appropriate to use a normal approximation to this binomial distribu- tion? Why? (b) Compute u and or of the approximating normal distribution. (c) Use a continuity correction factor to convert the statement r≥ 23 suc- cesses to a statement about the corresponding normal variable x. (d) Estimate P(r≥ 23). (e) Interpretation Is it unusual for a binomial experiment with 40 trials and probability of success 0.50 to have 23 or more successes? Explain.
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Transcribed Image Text:### Basic Computation: Normal Approximation to a Binomial Distribution
Suppose we have a binomial experiment with \( n = 40 \) trials and a probability of success \( p = 0.50 \).
(a) **Is it appropriate to use a normal approximation to this binomial distribution? Why?**
(b) **Compute \( \mu \) and \( \sigma \) of the approximating normal distribution.**
(c) **Use a continuity correction factor to convert the statement \( r \geq 23 \) successes to a statement about the corresponding normal variable \( x \).**
(d) **Estimate \( P(r \geq 23) \).**
(e) **Interpretation**: Is it unusual for a binomial experiment with 40 trials and a probability of success 0.50 to have 23 or more successes? Explain.
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