Statistics and Probability Answers

If a sample of 10 cups of ice cream is selected, what is the probability that the mean of the sample will be larger than 670 mg? 

Question :

The “Titans” cricket team has a winning rate of 75%. The team is planning to play 10 matches in the next season.

a)    Let X be the number of matches that will be won by the team. What are the possible values of X?

b)    What is the probability that the team will win exactly 6 matches?

c)    What is the probability that the team will lose 2 or less matches?

d)    What is the mean number of matches that the team will win?

e)    What are the variance and the standard deviation of the number of matches that the team will win?

Doubt in (c) = What is the probability that the team will lose 2 or less matches?

(Here, do we have to use P(X less than equal to 2)?

A dice is tossed 120 times with the following

results.

Number turned up 1 2 3 4 5 6 Total

Frequency 30 25 18 10 22 15 120

Test the hypothesis that the dice is un biased.

A restaurant owner is concerned about the amount of time customers must wait before being served over

weekends. He collects data on the waiting times, to the nearest minute, of 20 tables on Friday evening and

15 tables on Saturday evening.

The average waiting time on Friday evening is 24 minutes per table.

The total waiting time for the 15 tables on Saturday evening is seven hours and three

quarters of an hour.

The mean waiting time per table for Friday and Saturday evening, rounded to the nearest minute, is

The ages (in years) of 50 individuals on a mailing list, in ascending order are:

10 11 13 14 14 15 15 17 18 20

20 21 22 24 26 26 26 27 29 30

31 31 33 34 36 36 36 37 38 39

40 41 41 43 44 45 45 46 47 48

49 51 53 55 57 58 59 59 60 60

Consider the frequency table for the data:

A B C D

Interval Frequency Frequency Frequency Frequency

0,5 – 15,5 5 7 7 5

15,5 – 30,5 14 13 12 15

30,5 – 45,5 16 17 18 14

45,5 – 60,5 15 13 13 16

The column that represents the correct frequencies for the data is

[1] A

[2] B

[3] C

[4] D

A quality-control exercise was carried out by ChocCheer for estimating the percentage of defective chocolate

bars in a large shipment of 1 000 boxes with 100 bars in each box. Twenty boxes were chosen at random,

and every bar in them checked. The number of defective bars in each of the boxes are:

8, 10, 4, 3, 11, 6, 9, 10, 2, 7, 6, 12, 9, 11, 6, 3, 14, 9, 5, 4

Choose the CORRECT statement.

[1] The variable is the 1 000 boxes of chocolate bars.

[2] The sample unit 149.

[3] The sample is the 20 boxes of chocolate bars that were selected.

[4] The population is the 100 chocolate bars per box

1. A researcher wants to compare the performance of students living with their parents and

the performance of these students whose parents are working. Random samples were

taken from two normally distributed groups of population. 20 students who are living

with their parents posted an average grade of 89.25 with standard deviation of 2.4,

whereas the 15 randomly selected students whose parents are working abroad have an

average grade of 86.00 with standard deviation of 3.2. Test whether there is a significant

difference between the two groups of students at 0.05 level of significance.

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The probability to win a fund raising lottery is 0.3. What is the probability that exactly 2 out of 5 tickets win?

1. Louie wants to estimate the average value of the lot in his town with 99% confidence interval. Use his random sample of 36 lots with an average value of Php251, 131.42 and a standard deviation of Php1 321.467 to find the confidence interval.

2. A survey conducted for 200 students to determine if they need financial assistance in their studies, it found out that 168 of them needed this assistance. Find the 90% confidence interval for the population proportion of students needing loans or scholarships.