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- From Mathematics, Statistics
- Due on 08 Mar, 2016 05:51:00
- Asked On 08 Mar, 2016 02:42:37
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12. Use the normal distribution to approximate the binomial distribution and find

the probability of getting 15 to 18 heads out of 25 flips. Compare this to what

you get when you calculate the probability using the binomial distribution.

Write your answers out to four decimal places

60. What is the median recovery time? **Explain your answer**

a. 2.7

b. 5.3

c. 7.4

d. 2.1

70. Which of the following is NOT TRUE about the distribution for averages**? Explain your answer**

a. The mean, median, and mode are equal.

b. The area under the curve is one.

c. The curve never touches the x-axis.

d. The curve is skewed to the right.

62. Suppose that the distance of fly balls hit to the outfields (in baseball) is normally

distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly

sample 49 fly balls

What is the probability that the 49 balls traveled an average of less than 240 feet? **Sketch the graph**. Scale the horizontal axis for 𝑋̅. Shade the region corresponding to the probability. Find the probability

76. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.

b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? **Sketch the graph**. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability

66. Height and weight are two measurements used to track a child’s development. The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender. In 2009, weights for all 80 cm girls in the reference population had a mean µ = 10.2 kg and standard deviation σ = 0.8 kg. Weights are normally distributed. X ~ N(10.2, 0.8). **Calculate the z-scores that correspond to the following weights and interpret them**

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Use the normal distribution to approximate the binomial distribution and find the probability of getting 15 to 18 heads out of 25 flips. Compare this to what you get when you calculate the probability using the binomial distribution. Write your answers out to four decimal places.
Ans For the binomial distribution of coin flipping, probability of getting a head (success) in one flip = p = 0.5
N = no. of trials = 25
Mean is = N*p = 25 * 0.5 = 12.5
Variance σ2 = Np(1-p) = (25)(0.5)(0.5) = 6.25
The standard deviation is therefore σ = √6.25 = 2.5.
Using the binomial calculator (Lane CH-5),
the probability of getting 15 to 18 heads out of 25 flips = 0.2049
Using the normal distribution to approximate the binomial distribution: The area between 14.5 and 18.5 in the normal distribution curve is an approximation of the probability of obtaining 15 to 18 heads.
Area below 14.5 = 0.7881
Area below 18.5 = 0.9918
Therefore,
Area between 14.5 and 18.5 = 0.9918 – 0.7881 = 0.2037
So in this case,
the probability of getting 15 to 18 heads out of 25 flips = 0.2037
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.
What is the median recove...

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