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Molodets [167]
3 years ago
14

The proportion of American births that result in a birth defect is approximately 1/33 according to the Centers for Disease Contr

ol and Prevention (CDC). A local hospital randomly selects five births and lets the random variable X count the number resulting in a defect. Assume the births are independent. Identify an appropriate probability model for X. a. binomial distribution with n
Mathematics
2 answers:
Ksju [112]3 years ago
8 0

Answer:

BINOMIAL DISTRIBUTION

Step-by-step explanation:

To find out 'x' successes out of 'n' trials, Binomial Distribution is used.

Success = Birth Defect ;

  • Prob (success) = Prob (Birth defect) = 1/33 = 0.030
  • Prob (no success) = Prob (no birth defect) = 1- 0.030 = 0.97

n = total trials = 5 births (given)

Let 'x' be the no. of successes (defective births) out of 5 ;

P(n, x) = nCx p^x (1 - p)^(n - x)          

Eg, with given info :-  P (5,x) = 5Cx. (0.030)^x. (0.97)^ (n-x)

max2010maxim [7]3 years ago
7 0

Answer:

The appropriate probability model for X is a Binomial distribution,

X \sim Bin (<em>n</em> = 5, <em>p</em> = 1/33).

Step-by-step explanation:

The random variable <em>X</em> can be defined as the number of American births resulting in a defect.

The proportion of American births that result in a birth defect is approximately <em>p</em> = 1/33.

A random sample of <em>n</em> = 5 American births are selected.

It is assumed that the births are independent, i.e. a birth can be defective or not is independent of the other births.

In this experiment the success is defined as a defective birth.

The random variable <em>X</em> satisfies all criteria of a Binomial distribution.

The criteria are:

  • Number of observations is constant
  • Independent trials
  • Each trial has only two outcomes: Success and Failure
  • Same probability of success for each trial

Thus, the appropriate probability model for X is a Binomial distribution, Bin (<em>n</em> = 5, <em>p</em> = 1/33).

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