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find the area under the standard normal curve between z=0.52 and z=2.31
Test marks (%) obtained in a test are normally distributed with a mean of 55 % and variance of 400 (% squared).
what is the probability that a randomly selected student scored below 40%?
A normal distribution of scores has a variance of S squared = 100. Find the z-scores corresponding to each of the following values:
a) a score that is 20 points above the mean
b) a score that is 10 points below the mean
2) Given a mean score of 43 and a standard deviation of 5 for teaching readiness test among a sample of students calculate raw scores for the following:
a) a z-score of 1.50
b) a z-score of -2.00
3) Subjective wellbeing was measured among a sample of Statistics students with M=150 and S squared=25. Determine the z-scores for the students who obtained the following scores on the subjective wellbeing measure.
a) 110
b) 135
The Gauteng chamber of business conducted a survey amongst 17 furniture retailers to identify the percentage of bad debts in each company’s debtors’ book. The bad debts percentages are as follows:
2.2, 4.7, 6.3, 5.8, 5.7, 7.2, 2.6, 2.4, 6.1, 6.8, 2.2, 5.7, 3.4, 6.6, 1.8, 4.4, 5.4
Calculate the Pearson Coefficient of skewness coefficient for percentage of bad debts. Is the data skewed?
Suppose you roll a pair of dice. Let A be the event that you roll an even number. Let B be the event that you roll an odd number. Which of the following statements is true?
Select one:
a. The intersection of A and B is the empty set ∅.
b. The complement of event B is the set [1, 3, 5, 7, 9, 11].
c. The events A and B are not collectively exhaustive.
d. The events A and B are not mutually exclusive.
A bored carpenter counts the actual number of nails in 10 boxes of nails and records his findings as: 230, 235, 302, 287, 312, 323, 265, 319, 342, and 298. What can we say about the shape of the distribution of the number of nails?
Apply Regression Model and find out b0 and b1, additionally, try to find out Karl
Person’s Correlation Coefficient. Write the interpretation covering correlation and
estimated quantities in regression analysis (b0 and b1 only).
The below given table show the Region wise sales of Govind Chips, the data is
collected for 26 districts of Gujarat. Reference period of this data is 2019-2020.
ales figures are in lakhs and spending in advertisement is also given in Lakhs.
District Sales(00,000' INR) Amount spending in Advertisement(00,000'INR)
Kachchh 40 3.6
Banas Kantha 19 2.1
Patan 20 2.2
Mahesana 30 2.5
Sabar Kantha 27 2.3
Gandhinagar 50 6
Ahmadabad 49 5
Surendranagar 26 2.3
Rajkot 45 3.7
Jamnagar 48 3.8
Porbandar 14 1.7
Junagadh 44 3.6
Amreli 32 2.8
Bhavnagar 29 2.3
Anand 33 3
Kheda 14 1.8
Panch Mahals 45 3.9
Dohad 13 1.5
Vadodara 49 4.5
Narmada 25 2
Bharuch 39 3.5
The Dangs 11 1
Navsari 18 2
Valsad 30 2.9
Surat 48 4
Tapi 17 1.9
a) 10000 ‘Roshani’ light bulbs with a mean life of 150 days are installed in a new factory
and their length of life is normally distributed with standard deviation of 10 days.
How many Roshani-bulbs will expire in less than 160 days?
b) Plot the appropriate Graph. Here, objective is to show the linear relationship between
the sales of the product and amount spent in advertisement of a certain product.
Based on the graphical output write your comment on linear association between these
two variables.
Note: Participants may use MS-EXCEL, or they may prepare it on a piece of paper.
Region Sales(000'INR) Amount spent in Advertisement (000'INR)
1 260.3 5
2 286.1 7
3 279.4 6
4 410.8 9
5 438.2 12
6 315.3 8
7 565.1 11
Three airlines is providing services in Rajkot, a city in Gujarat. Airline
‘Saras’ has 50% of all the scheduled flights, airline ‘Yug’ has 30%, and airline
‘Pushpak’ has the remaining 20%. Their on-time rates are 80%, 65%, and 40%,
respectively.
A plane has just left on time from Rajkot Airport. What is the probability that it will
reach to its destination on time?
Note: It is mandatory to Prepare Probability Tree Diagram
Suppose it is assumed that a linear relationship exists between n observations of the response
variable Yi and a predictor variable Xi .
(a) Name and state the regression model for this scenario.
