Use the appropriate normal distribution to approximate the resulting binomial distribution. A marksman's chance of hitting a target with each of his shots is 75%. (Assume the shots are independent of each other.) If he fires 40 shots, what is the probability of his hitting the target in each of the following situations? (Round your answers to four decimal places.) (a) at least 35 times (b) fewer than 25 times (c) between 27 and 35 times, inclusive

Use the appropriate normal distribution to approximate the resulting binomial distribution. A marksman's chance of hitting a target with each of his shots is 75%. (Assume the shots are independent of each other.) If he fires 40 shots, what is the probability of his hitting the target in each of the following situations? (Round your answers to four decimal places.) (a) at least 35 times (b) fewer than 25 times (c) between 27 and 35 times, inclusive

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Use the appropriate normal distribution to approximate the resulting binomial distribution.

A marksman's chance of hitting a target with each of his shots is 75%. (Assume the shots are independent of each other.) If he fires 40 shots, what is the probability of his hitting the target in each of the following situations? (Round your answers to four decimal places.)

(a) at least 35 times

(b) fewer than 25 times

(c) between 27 and 35 times, inclusive

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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