Daytime high temperatures in New York in February are normally distributed with an average of 30.2º and a standard deviation of 8.5º.
Estimate the probability that the temperature on a given day in February is 39º or higher.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
0.23
4) The data below illustrates the movements of a portfolios annual returns over a 12-year period. (To get full points you must show all your working)
Portfolio movements, 2002-2013(%)
2002 -7.14
2003 1.62
2004 2.48
2005 -2.59
2006 9.37
2007 -0.55
2008 -0.89
2009 -9.19
2010 -5.11
2011 -0.49
2012 6.84
2013 3.04
To estimate the probability that the temperature on a given day in February is 39º or higher, we can use the concept of the standard normal distribution, also known as the Z distribution.
Step 1: Standardize the value of 39º using the formula:
Z = (X - μ) / σ
where:
- Z is the standard score
- X is the value we want to standardize (39º in this case)
- μ is the mean of the distribution (30.2º in this case)
- σ is the standard deviation of the distribution (8.5º in this case)
Substituting the values, we get:
Z = (39 - 30.2) / 8.5
Step 2: Calculate the probability using the standard normal distribution table or a statistical calculator. Look up the Z-value obtained in step 1 and find the corresponding probability. In this case, we want to find the probability of getting a Z-value equal to or greater than the one we calculated.
For example, if we find that the Z-value is 0.96, we can look up this value in the standard normal distribution table or use a calculator to find the probability associated with it. Let's assume that the probability is P(Z ≥ 0.96) = 0.8315.
Therefore, the estimated probability that the temperature on a given day in February is 39º or higher is 0.8315 or 83.15%.