Question

1. Weakly earnings on a certain import venture are approximately normally distributed with a known mean of $487 and unknown standard deviation. If the proportion of earnings over $517 is 27%, find the standard deviation. Answer only up to two digits after decimal.

2.X is a normal random variable with mean μ and standard deviation σ. Then P( μ− 1.4 σ ≤ X ≤ μ+ 2.2 σ) =? Answer to 4 decimal places.

3.Suppose X is a Binomial random variable with n = 32 and p = 0.41.

Use binomial distribution to find the exact value of   P(X < 11). [Answer to 4 decimal places]

错误.

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以前的尝试

What are the appropriate values of mean and standard deviation of the normal distribution used to approximate the binomial probability?
μ = 13.12, and σ = 0.087.
μ = 13.12, and σ = 2.782.
μ = 13.12, and σ = 7.741.
μ = 32, and σ = 0.41.

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Using normal approximation, compute the approximate value of   P(X < 11). [Answer to 4 decimal places]

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Is the n sufficiently large for normal approximation?
Yes, because n is at least 30.
No, because μ±3σ, is contained in the interval (0, 32).
Yes, because μ±3σ, is inside the interval (0, 32).
No, because np < 15

4. Usually about 65% of the patrons of a restaurant order burgers. A restaurateur anticipates serving about 155 people on Friday. Let X be the numbers of burgers ordered on Friday. Then X is binomially distributed with parameters n = 155 and p = 0.65.

What is the expected number of burgers (μ_X) ordered on Friday? [Answer up to 2 digits after decimal]

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Find the standard deviation of X (σ_X)? [Answer up to 3 digits after decimal]

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If the restaurant ordered meats to prepare about 109 burgers for Friday evening. Use normal approximation of binomial distribution to find the probability that on Friday evening some orders for burgers from the patron cannot be met. [Answer up to 4 digits after decimal]

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How many burgers the restaurant should prepare beforehand so that the chance that an order of burger cannot be fulfilled is at most 0.05? i.e. Find a such that P(X > a) = 0.05 using normal approximation of binomial distribution.

Answer 1

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