5. NBC News reported on May 2, 2013, that 1 in 20 child United States have a food allergy of some sort. Conside random sample of 25 children and let X be the number who have a food allergy. Then X-Bin(25, 05). (Show even though you can find the answers from the calculat a) Determine P(X = 3), P(X ≤ 3) and P(X<3). b) Determine P (X24). c) Determine P(1 ≤ x ≤ 3). d) What are E(X), E(X) and o₂?

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Question 5
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5. NBC News reported on May 2, 2013, that 1 in 20 children in the
United States have a food allergy of some sort. Consider selecting a
random sample of 25 children and let X be the number in the sample
who have a food allergy. Then X-Bin(25, .05). (Show your work,
even though you can find the answers from the calculator.)
a) Determine P(X= 3), P(X ≤ 3) and P(X<3).
b) Determine P (X24).
c) Determine P(1 ≤ x ≤ 3).
d) What are E(X), E(X²) and o₂?
e) In a sample of 50 children, what is the probability that none has a food
allergy?
6. A particular telephone number is used to receive both voice calls and
fax messages. Suppose that 25% of the incoming calls involving fax
messages, and consider a sample of 25 incoming calls. [Hint: Is this a
binomial distribution? (Show your work, even though you can find the
answers from the calculator.)]
a)
What is the probability that
(1) At most 6 of the calls involve a fax message?
(11) Exactly 6 of the calls involve a fax message?
(111) At least 6 of the calls involve a fax message?
(iv) More than 6 of the calls involve a fax message?
b) What is the expected number of calls involving a fax message in the
sample? (Do not round your answer.)
3
Transcribed Image Text:Page 5. NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 25 children and let X be the number in the sample who have a food allergy. Then X-Bin(25, .05). (Show your work, even though you can find the answers from the calculator.) a) Determine P(X= 3), P(X ≤ 3) and P(X<3). b) Determine P (X24). c) Determine P(1 ≤ x ≤ 3). d) What are E(X), E(X²) and o₂? e) In a sample of 50 children, what is the probability that none has a food allergy? 6. A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involving fax messages, and consider a sample of 25 incoming calls. [Hint: Is this a binomial distribution? (Show your work, even though you can find the answers from the calculator.)] a) What is the probability that (1) At most 6 of the calls involve a fax message? (11) Exactly 6 of the calls involve a fax message? (111) At least 6 of the calls involve a fax message? (iv) More than 6 of the calls involve a fax message? b) What is the expected number of calls involving a fax message in the sample? (Do not round your answer.) 3
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