Question

It has been estimated that about 30% of frozen chickens contain enough salmonella...continues

It has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozenchickens. What is the probability that the consumer will have no more than 6 contaminated chickens?
(a) 0.961
(b)0.118
(c)0.882
(d)0.039
(e)0.079

Refer to the previous question. Suppose that a supermarket buys 1000 frozen chickens from a supplier. The number of frozen chickens that may be contaminated that arewithin two standard deviations of the mean is between A and B. The numbers A and B are
(a) (90,510)
(b) (290.8,309.2)
(c) (0,730)
(d) (271,329)
(e) (255,345)
2 2
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Answer #1
Concepts and reason

A binomial distribution is a type frequency distribution used when there are exactly two outcomes from each trial (either a success or failure)

Fundamentals

The density function of Binomial distribution is,

--ar
Р(х -х)-
х%3D0,1, 2, ..., п
(1-р);
х

The probability of a success is the same for each trial

The trails are random and independents (outcome of one has no bearing on the outcome of another trial)

The empirical rule describes the 2 standard deviation formula is, (u20)

Here, represents the population mean

represents the population standard deviation.

The correct option is: A

From the given information we have0.30
n 12 and p 30%

Let X
denote the contaminated chickens.

Calculate the probability that the consumer will have no more than 6 contaminated chickens.

P(X 6)
P(X0)+P(X )+.+P(X 6)
(12
12
(0.30) (1-0.30)
-(0.30) (1-0.30)
0.01384..+0.07925
=0.96140
(Round to 3 decimal place)
0.9

The correct option is: D

The available information is: n 1000 and p 0.30

Calculate the mean and standard deviation.

Мean(u) — пр
1000x0.30
300

Standard deviation (o)= /np(1-p)
|1000x0.30(1-0.30)
14.49138
(Round to 2 decimal place)
14.49

Calculate the two standard deviation mean is between | A and B

2standard deviation limits = u± 2
=300+2 (14.49)
=300t28.98
=271.02,328.98
(271,329)
(Round to nearest whole number)

Ans:

The probability is 0.961

The value of A and B
is 217 and 329.

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Answer #2
1 ans) Given that It has beenestimated that about 30% of frozen chicken contain enoughsalmonella bacteria to cause illness if improperly cooked
ie p = 0.30
A consumerpurchases 12(n) frozen chickens.
which follows a binomial distribution then
the probability that the consumer will have morethan 6 contaminated chickens is given by


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