Question

The mean temperature for the month of July in Boston, Massachusettsis 73 degrees Farenheit. Plot the following data, which represent the observed mean temperature in Boston over the last 20 years.

1998 7 999 69 2000 78 2001 70 2002 67 2003 74 2004 73 2005 65 2006 77 2007 71 2008 75 2009 68 2010 72 2011 77 2012 65 2013 79 2014 77 2015 78 2016 72 a. Is this a normal distribution? Explain your reasoning. b. What is an outlier? Are there any outliers in this distribution? Explain your reasoning fully. c. Using the above data, what is the probability that the mean will be over 76 in any given July? d. Using the above data, what is the probability that the mean will be over 80 in any given July?

Answer 1

Solution :

Plot of given data is as

頓R Graphics: Device?IACTVE) 2010 2005 2015 2000

R Console x1998:2017 y-c(72, 69, 78, 70, 67,74-73,65, 77,71/ 75, 68 72, 77, 65,79,77, 78, 72, 74) plot ( y) > shapiro.test (y) Shapiro-Wilk norrmality test data: V therefore mean temperature ie normaIvi distribute
b)

Outliers is the value in given data set ( observed value ) which lies an abnormal distance from other values in data set . It also know as extreme point .

62.5 84.25

In our given data set all values lies between 62.5 and 84.25 .so there is not any outliers in given data set.

above solution is correct with full explaination so please rate me high.

l the probabili tr t 1 :76 n any given July 13 т hi l e n ra E L > #Q.d) the probability t;hat the mean will be over-76 in any given july is