1. Weakly earnings on a certain import venture are approximatelynormally distributed with a known mean of $487 and unknown standarddeviation. If the proportion of earnings over $517 is 27%, find thestandard deviation. Answer only up to two digits after decimal.
2.X is a normal random variable with mean ? andstandard deviation ?. Then P( ?? 1.4 ? ? X ? ?+2.2 ?) =? Answer to 4 decimal places.
3.Suppose X is a Binomial random variable withn = 32 and p = 0.41.
Use binomial distribution to find the exact value of P(X < 11). [Answer to 4 decimalplaces]
What are the appropriate values of mean and standard deviationof the normal distribution used to approximate the binomialprobability?
? = 13.12, and ? = 0.087.
? = 13.12, and ? = 2.782.
? = 13.12, and ? = 7.741.
? = 32, and ? = 0.41.
Using normal approximation, compute the approximate value of P(X < 11). [Answer to 4 decimalplaces]
Is the n sufficiently large for normalapproximation?
Yes, because n is at least 30.
No, because ?±3?, is contained in the interval (0, 32).
Yes, because ?±3?, is inside the interval (0, 32).
No, because np < 15
4. Usually about 65% of the patrons of a restaurant orderburgers. A restaurateur anticipates serving about 155 people onFriday. Let X be the numbers of burgers ordered on Friday.Then X is binomially distributed with parametersn = 155 and p = 0.65.
What is the expected number of burgers (?X)ordered on Friday? [Answer up to 2 digits after decimal]
Find the standard deviation of X(?X)? [Answer up to 3 digits after decimal]
If the restaurant ordered meats to prepare about 109 burgers forFriday evening. Use normal approximation of binomial distributionto find the probability that on Friday evening some orders forburgers from the patron cannot be met. [Answer up to 4 digits afterdecimal]
How many burgers the restaurant should prepare beforehand sothat the chance that an order of burger cannot be fulfilled is atmost 0.05? i.e. Find a such that P(X> a) = 0.05 using normal approximation of binomialdistribution.
