Question 1

A manufacturing plant claims that only 0.2% of its products are defective.From a sample of 3000 products,it is found that 4 are defective.Using n = 3000 and p = 0.002,approximate P(X = 4)by using the normal approximation.

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The answer of A manufacturing plant claims that only 0.2%...

Question 2

Suppose X has a binomial distribution with n = 100 and p = 0.1.Using the normal approximation,find

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The answer of Suppose X has a binomial distribution with...

Question 3

Suppose X has binomial distribution with n = 100 and p =  
.Using the normal approximation,find (a)  
and (b)

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The answer of Suppose X has binomial distribution with n...

Question 4

Playing a fair "shell game," the probability of winning the game should be given by p =  
.One person plays the game 50 times but only wins 7 times.Using n = 50,approximate P(X = 7)by using the normal approximation.

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The answer of Playing a fair "shell game," the probability...

Question 5

If X is normally distributed with μ = 90 and σ = 10,find P(65 < X < 80).

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The answer of If X is normally distributed with μ...

Question 6

A professor claims that there is only a 15% chance of earning an "A" in her class.At the end of the semester,40 of the 278 students earn "A's." Using n = 278 and p = 0.15,approximate P(X = 40)by using the normal approximation.

Accepted Answer

The answer of A professor claims that there is only...

Question 7

Suppose X has binomial distribution with n = 100 and p = 0.1.Using the normal approximation,find (a)  
and (b)

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The answer of Suppose X has binomial distribution with n...

Question 8

If a fair coin is tossed 100 times,use the normal approximation to estimate the probability of getting at least 60 heads.

Accepted Answer

We can use the normal approximation to estimate the probability of getting at least 60 heads. We know that the mean of a binomial distribution is np = 100(0.5) = 50 and the standard deviation is sqrt(np(1-p)) = sqrt(100(0.5)(0.5)) = 5.

To use the normal approximation, we need to standardize the value of 60 using the formula z = (x - mu) / sigma, where x is the number of heads, mu is the mean, and sigma is the standard deviation.

z = (60 - 50) / 5 = 2

We can now use a standard normal table or calculator to find the probability of getting a z-score of 2 or more.

Using a standard normal table, we find that P(Z ≥ 2) = 0.0228.

Therefore, the answer is A: 0.0287.

Quiz 17: Continuous Random Variables

A manufacturing plant claims that only 0.2% of its products are defective.From a sample of 3000 products,it is found that 4 are defective.Using n = 3000 and p = 0.002,approximate P(X = 4)by using the normal approximation.

Suppose X has a binomial distribution with n = 100 and p = 0.1.Using the normal approximation,find

Suppose X has binomial distribution with n = 100 and p = .Using the normal approximation,find (a) and (b)

Playing a fair "shell game," the probability of winning the game should be given by p = .One person plays the game 50 times but only wins 7 times.Using n = 50,approximate P(X = 7)by using the normal approximation.

If X is normally distributed with μ = 90 and σ = 10,find P(65 < X < 80) .

A professor claims that there is only a 15% chance of earning an "A" in her class.At the end of the semester,40 of the 278 students earn "A's." Using n = 278 and p = 0.15,approximate P(X = 40)by using the normal approximation.

Suppose X has binomial distribution with n = 100 and p = 0.1.Using the normal approximation,find (a) and (b)

If a fair coin is tossed 100 times,use the normal approximation to estimate the probability of getting at least 60 heads.