# Quantitative Analysis: 954657

Problem 1

 Temperature Frequency Cumulative % 62 0 0.00% 64 0 0.00% 66 2 10.53% 68 2 21.05% 70 2 31.58% 72 3 47.37% 74 3 63.16% 76 1 68.42% 78 5 94.74% 80 1 100.00% 82 0 100.00% More 0 100.00%

Figure 1: A frequency distribution table for mean temperature in Boston

The distribution has a long tail to the left, hence it is skewed to the left.

 Year(n) Mean (x) x^2 p(x) x.p(x) x^2.P(x) 1998 72 5184 0.04955 3.56779 256.881 1999 69 4761 0.04749 3.27667 226.090 2000 78 6084 0.05368 4.18720 326.602 2001 70 4900 0.04818 3.37233 236.063 2002 67 4489 0.04611 3.08947 206.994 2003 74 5476 0.05093 3.76875 278.888 2004 73 5329 0.05024 3.66758 267.734 2005 65 4225 0.04474 2.90778 189.006 2006 77 5929 0.05299 4.08052 314.200 2007 71 5041 0.04886 3.46937 246.326 2008 75 5625 0.05162 3.87130 290.348 2009 68 4624 0.04680 3.18238 216.402 2010 72 5184 0.04955 3.56779 256.881 2011 77 5929 0.05299 4.08052 314.200 2012 65 4225 0.04474 2.90778 189.006 2013 79 6241 0.05437 4.29525 339.325 2014 77 5929 0.05299 4.08052 314.200 2015 78 6084 0.05368 4.18720 326.602 2016 72 5184 0.04955 3.56779 256.881 2017 74 5476 0.05093 3.76875 278.888 Sum of Temp 1453 µ 72.8968 Std 4.2341 Max 79 Min 65 Range 14 ∑p(x) 1 ∑X^2.P(x) 5331.5148

The data above is normally distributed because the sum of individual probabilities is 1.

b) An outlier can be defined as an observation point which is distant from the rest of the observations.

c)

To identify outliers, we would plot a scatter plot of average temperature against time(years).

Figure 2: A scatter plot for mean temperature data in Boston.

From the above figure, it is evident that there are no outliers’ data.

d)

Given, µ=73.0  ,

Now computing the test statistics using the formula

Now P(Z<

Then, P(Z>

Therefore, the what is the probability that the mean will be over 76 in any given July is .
e)

Given the following values.

µ=73.0  ,

Using the formula   to compute test statistics

Now we can compute P(Z<

Computing P(Z>

Therefore, the probability that the mean will be over 80 in any given July is

Problem 2

 Temp Range Frequency Cumulative % 82 0 0.00% 84 1 5.26% 86 4 26.32% 88 4 47.37% 90 5 73.68% 92 5 100.00% 94 0 100.00% 96 0 100.00% More 0 100.00%

Figure 3: A frequency graph for heatwave temperature.

From the given heat wave data, the following calculations are obtained.

 Days(n) Temp (x) p(x) x.p(x) 1 93 0.05234 4.867192 2 88 0.04952 4.357907 3 91 0.05121 4.660101 4 86 0.04840 4.162071 5 92 0.05177 4.763084 6 91 0.05121 4.660101 7 90 0.05065 4.558244 8 88 0.04952 4.357907 9 85 0.04783 4.065841 10 91 0.05121 4.660101 11 84 0.04727 3.970737 12 86 0.04840 4.162071 13 85 0.04783 4.065841 14 90 0.05065 4.558244 15 92 0.05177 4.763084 16 89 0.05008 4.457513 17 88 0.04952 4.357907 18 90 0.05065 4.558244 19 88 0.04952 4.357907 20 90 0.05065 4.558244 n=20 Sum 1777 1 88.922341
 Mean 88.85 Median 89.5 Mode 88 n 20 Max 93 Min 84 Range 9

The data has a normal distribution because mean, median and mode are fairly the same.

Heat wave ~three or more days with a high temperature over 90 degrees Fare height.

P(n≥10)=P(n=12)*p(n=15)*p(n=18)

P(n≥10)= 0.04840 *0.05177 *0.05065=0.0001269

The probability that the heat wave will have a temperature more than 90  in three interval days is 0.0001269

Problem 3

a) The situation of the customers’ behavior exactly fits the parameters for a binomial distribution. This is because of exactly 2 possible outcomes of occurrences from the customers’ behavior to either buy online or from the physical store. There is no any other possible alternative among customers in the market, despite when the occurrence is repeated on multiple times.

b) P (customers purchase online) =40%

=40/100

=0.4

P (Customers purchase from the physical store )=60%

=60/100

=0.6

c) P (Exactly four sales bought online each day =4/12

=1/3

0.3333.

d) P (From 12 sales made each day, fewer than 6 are made online=1-P(6 sales are made     online)

=1-6/12

=1-0.5

=0.5

e) From the 12 sales made each day    more than 8 are made online =1-P(8sales are made online)

=1-8/12

=1-2/3

=1/3

=0.3333.

Problem 4

a)

My company of choice is Apple Company. According to an article written by Adrian Kinsley on December 29 2018, Apple company made it clear that it would no longer report on iPhone, iPad and mac books unit sales as their objective is to make great products for customer satisfaction. However, this had sparked fears among Apple investors who are now believing that things are not going well for the company. This is because both the iPhone and smartphone sales have been weakening as people no longer buy the iPhone their new features but rather than but rather to change the older used phones. Smartphones have also become dull and Apple is keen on coming up with more exciting features. Together with trump tariff of 10%, tariff increment on Chinese made phones and mac books. Considering the above problems facing the company, Apple has a lot to do in convincing the customer to buy their expensive iPhones so as to maintain a constant revenue (Kinsley, 2018).

b)

I would carry out market analysis research.

The data to be collected Customer’s age, Customer’s Income, region etc.

c)

The data would be a poison’s distribution.

This is because the collected data are both discrete and continuous.

d)

Customers’ buying trends and customer’s average age that use iPhone.

e)

The aim of every business is to make profits while providing quality products to their esteem customers. Once, the customer is satisfied with the product, their willingness to pay even for higher costing products increases. The company, therefore, needs to provide funds for data collection and analysis failure to which the company will incur losses.

Refence

Livak, K. J., & Schmittgen, T. D. (2001). Analysis of relative gene expression data using real-time quantitative PCR and the 2− ΔΔCT method. methods25(4), 402-408.

Ramakers, C., Ruijter, J. M., Deprez, R. H. L., & Moorman, A. F. (2003). Assumption-free analysis of quantitative real-time polymerase chain reaction (PCR) data. Neuroscience letters339(1), 62-66.

A. K. (2018, December 29). Challenges fcing Apple in 2019. Hughes for Hardware 2.0.