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Probability - normal distribution

1. If a fair coin is tossed 20 times then the probability of exactly 10 Tails is more than 15 percent.

2. The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population, what is the probability that it will weigh less than 904 grams?

3. About 12% of the customers of a store buy cigars and 20 % of customers buy beer. the contingency table is given below.
Beer No Beer
Cigars .08 .04 .12
No cigar .12 .76 .88
.20 .80 1.0
Determine the probability that a customer will buy at least one of these items: cigar or beer.

4. A door-to-door sales person for a Household appliance has learned from her past experience that out of twenty demonstrations of her appliance only seven result in actual sales (long run average). This week she needs to make at least four sales. At least how many demonstrations does she need to perform to ensure that the probability of meeting her target is at least 95 percent?

5. If x is a binomial random variable where n=100 and p=.1, find the probability that x is less than or equal to 12 using the normal approximation to the binomial.

6. The weight of a product is normally distributed with a standard deviation of .6 ounces. What should the average weight be if the production manager wants no more than 5% of the products to weigh more than 8 ounces?

Solution Preview

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Help with practice problems
1. If a fair coin is tossed 20 times then the probability of exactly 10 Tails is more than 15 percent.
Answer
Let X be the number of tails. Clearly X is binomial with n = 20 and p = 0.50. The probability mass function binomial variable is given by .The probability for different values of x are given below.
P (exactly 10 Tails) = P (X = 10)
=
= 0.1762
Hence the given statement is correct.

2. The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population, what is the probability that it will weigh less than 904 grams?
Answer
Let X be the fill weight of the adult cereal. Given that X is normal with mean µ = 910 and standard deviation  = 5.
We need P (X < 904). Standardizing the variable X using and from standard normal tables, we have,
P (X < 904) = = P (Z < ...

Solution Summary

The probability of coin tosses being tails is determined.

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