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In: Statistics and Probability

According to the National Institute of Allergy and Infectious Diseases, approximately 6% of U.S. children 4...

According to the National Institute of Allergy and Infectious Diseases, approximately 6% of U.S. children 4 years of age or younger have a food allergy. A day care program has capacity for 10 children in that age range. Assume that the children attending the day care program are independent. Let the random variable X be the number of children in this day care who have a food allergy.

1. Which distribution does X follow?

a. Normal distribution with mean 8 and variance 0.07

b. Binomial distribution with n = 10 and p = 0.94

c. Binomial distribution with n = 10 and p = 0.06

d. Poisson distribution with mean and variance 0.07

2. What are the approximate values of the mean and standard deviation of the distribution of X?

a. Mean = 0.08 and standard deviation = 0.0049

b. Mean = 0.60 and standard deviation = 0.7509

c. Mean = 0.60and standard deviation = 0.564

d. Mean = 0.56 and standard deviation = 0.7217

3. What is the probability that at most/best 4 children have a food allergy?

a. 0.9998

b. 0.9988

c. 0.1250

d. 0.0700

4. What is the probability that at least one of the ten children has a food allergy?

a. 0.8965

b. 0.5596

c. 0.4425

d. 0.4614

5. What is the probability P(X < 2)?

a. 0.9853

b. 0.8965

c. 0.8824

d. 0.8884

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orchestra answered 1 year ago

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