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A buoy floating in the ocean is bobbing in simple harmonic motion with period 6 seconds and amplitude 20cm. Its displacement d from sea level at time =t0 seconds is 0cm, and initially it moves downward. (Note that downward is the negative direction.)Give the equation modeling the displacement d as a function of time t.
For a standard normal distribution, find:
P(-2.43 < z < -1.87)
For a standard normal distribution, find: P(-2.43 <z<-1.87) Submit License Question 3. Points possible: 1 This is attempt 1 of 3.
Use Table A to find the proportion of observations from a
standard Normal distribution that satisfies each of the following
statements. Enter your answers rounded to four decimal
places.
a) z < -0.48 = b) z > -1.67 = c) z < 2.14 = d) – 0.48 < z < 2.14 =
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14. (3.28) Find the proportion of observations (±0.0001) from a standard Normal distribution that falls in each of the following regions. In each case, sketch a standard Normal curve and sha the area representing the region. (a)z -2.33: (b)-2.33 (c)z 1.55 (d)-2.33 <z<1.55:
4. Let X1, X2, ...,Xn be a random sample from a normal distribution with mean 0 and unknown variance o2. (a) Show that U = <!-, X} is a sufficient statistic for o?. [4] (c) Show that the MLE of o2 is Ô = 2-1 X?. [4] (c) Calculate the mean and variance of Ô from (b). Explain why ő is also the MVUE of o2. [6]
For a standard normal distribution, find: P(-1.95<z<0.09)
For a standard normal distribution, find: P(0.61 < z < 2.92)
Solve applications involving probabilities and corresponding x-scores for a normal distribution The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 30 days. If 144 women are randomly selected, find the probability that they have a mean pregnancy between 266 days and 268 days