: A government agency reports that 21% of baby boys 6-8 months old in the United States weigh less than 26 pounds. A sample of 148 babies is studied. Use the TI-84 Plus calculator as needed. Round the answer to at least four decimal places.(a) Approximate the probability that less than 38 babies weigh less than 26 pounds.(b) Approximate the probability that 36 or fewer babies weigh less than 26 pounds.(c) Approximate the probability that the number of babies who weigh less than 26 pounds is between 29 and 39 exclusive.Part: 0 / 30 of 3 Parts CompletePart 1 of 3The probability that less than 38 babies weigh less than 26 pounds is .
Question
: A government agency reports that 21% of baby boys 6-8 months old in the United States weigh less than 26 pounds. A sample of 148 babies is studied. Use the TI-84 Plus calculator as needed. Round the answer to at least four decimal places.(a) Approximate the probability that less than 38 babies weigh less than 26 pounds.(b) Approximate the probability that 36 or fewer babies weigh less than 26 pounds.(c) Approximate the probability that the number of babies who weigh less than 26 pounds is between 29 and 39 exclusive.Part: 0 / 30 of 3 Parts CompletePart 1 of 3The probability that less than 38 babies weigh less than 26 pounds is .
Solution
To solve this problem, we will use the binomial probability formula:
P(X = k) = C(n, k) * (p^k) * ((1-p)^(n-k))
where:
- P(X = k) is the probability we are trying to find,
- C(n, k) is the number of combinations of n items taken k at a time,
- p is the probability of success (in this case, the probability that a baby weighs less than 26 pounds, which is 21% or 0.21),
- n is the number of trials (in this case, the number of babies, which is 148), and
- k is the number of successes we are interested in.
(a) To find the probability that less than 38 babies weigh less than 26 pounds, we need to find the sum of the probabilities for 0, 1, 2, ..., 37 babies. This can be done using the binomial cumulative probability function on the TI-84 Plus calculator. The command is binomcdf(n, p, k), so in this case, we would enter binomcdf(148, 0.21, 37).
(b) To find the probability that 36 or fewer babies weigh less than 26 pounds, we would enter binomcdf(148, 0.21, 36) into the calculator.
(c) To find the probability that the number of babies who weigh less than 26 pounds is between 29 and 39 exclusive, we need to find the difference between the cumulative probabilities for 38 and 28 babies. This can be done by entering binomcdf(148, 0.21, 38) - binomcdf(148, 0.21, 28) into the calculator.
Please note that the actual values of these probabilities will depend on the specific values stored in your calculator, so I cannot provide the exact decimal values.
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