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According to studies, 1% of all patients who undergo laser surgery to correct their vision have serious post laser vision problems. In a random sample of 100,000 patients, let x be the number who experience serious post-laser vision problems. a. Find E(x). b. Find Var(x). c. Find the z-score for x = 950. d. Find the approximate probability that fewer than 950 patients in a sample of 100,000 will experience serious post-laser vision problems. First calculate the following interval. μ±3σ = np± 3√/pq If the interval lies in the range from 0 to n, the normal distribution will provide a reasonable approximation to the probabilities of most binomial events. Then express the binomial probability to be approximated in the form P(x≤a). For each value of interest, a, the correction for continuity is (a + .5) and the corresponding standard normal z value is the following. (a+.5)-μ z= σ

According to studies, 1% of all patients who undergo laser surgery to correct their vision have serious post laser vision problems. In a random sample of 100,000 patients, let x be the number who experience serious post-laser vision problems. a. Find E(x). b. Find Var(x). c. Find the z-score for x = 950. d. Find the approximate probability that fewer than 950 patients in a sample of 100,000 will experience serious post-laser vision problems. First calculate the following interval. μ±3σ = np± 3√/pq If the interval lies in the range from 0 to n, the normal distribution will provide a reasonable approximation to the probabilities of most binomial events. Then express the binomial probability to be approximated in the form P(x≤a). For each value of interest, a, the correction for continuity is (a + .5) and the corresponding standard normal z value is the following. (a+.5)-μ z= σ

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 42PFA
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Please help answer questions c and d. Ex = 1000; Var(x) = 990. Solve for the​ z-score for x = 950.

Find the approximate probability that fewer than 950 patients in a sample of 100,000 will experience serious​ post-laser vision problems

According to studies, 1% of all patients who undergo laser surgery to correct their vision have serious post laser vision problems. In a random sample of 100,000 patients, let x be the number who experience serious post-laser vision problems. a. Find E(x). b. Find Var(x). c. Find the z-score for x = 950. d. Find the approximate probability that fewer than 950 patients in a sample of 100,000 will experience serious post-laser vision problems.
Transcribed Image Text:According to studies, 1% of all patients who undergo laser surgery to correct their vision have serious post laser vision problems. In a random sample of 100,000 patients, let x be the number who experience serious post-laser vision problems. a. Find E(x). b. Find Var(x). c. Find the z-score for x = 950. d. Find the approximate probability that fewer than 950 patients in a sample of 100,000 will experience serious post-laser vision problems.
First calculate the following interval. μ±3σ = np± 3√/pq If the interval lies in the range from 0 to n, the normal distribution will provide a reasonable approximation to the probabilities of most binomial events. Then express the binomial probability to be approximated in the form P(x≤a). For each value of interest, a, the correction for continuity is (a + .5) and the corresponding standard normal z value is the following. (a+.5)-μ z= σ
Transcribed Image Text:First calculate the following interval. μ±3σ = np± 3√/pq If the interval lies in the range from 0 to n, the normal distribution will provide a reasonable approximation to the probabilities of most binomial events. Then express the binomial probability to be approximated in the form P(x≤a). For each value of interest, a, the correction for continuity is (a + .5) and the corresponding standard normal z value is the following. (a+.5)-μ z= σ
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