Math Answers

According to IT department of leading financial firm, 50% of emails received by their employees are spam. They are planning to install a software which filters the spam emails. A reputable cybersecurity brand has launched a software which claims to detect 99% of spam emails. However, they have also reported 5% as the chance of detecting a nonspam email as spam. If an email is detected as spam, what is the probability of it in fact being a non-spam email? 

Rohini has 3 scarfs which are identical in shape, form and cloth material. They are only different in colours. The first scarf is coloured red on both sides while both the sides of second scarf are coloured black. The third scarf is coloured black on one side and red on the other. She mixes the 3 scarfs in a box and randomly selects one scarfs and puts it down on the ground. If the upper side of the selected scarf is red in colour, what is the probability of the other side of the scarf to be black?

JGU students recently conducted a study to record the height of Asian Females in Haryana. They found the heights to be normally distributed with a mean 66 inches and a standard deviation of 2.5 inches.

a. Suppose a female is randomly selected. What is the probability of her height being between 65 and 69 inches.

b. Is it possible to meet a female in Haryana with a height more than 72 inches?

In 2016, around 12 Lakh students gave the CAT to bag an admission in India’s best business schools. In the math section of CAT, the marks follow a normal distribution with mean 520 and standard deviation 115.

A. What CAT score will be 1.5 standard deviations above the mean?

b. In 2022, a significant number of students also gave GMAT. Some colleges in India also accept GMAT scores as an alternative to CAT. The math section of GMAT is normally distributed with mean 21 and standard deviation 5.3. The math section is CAT-2022 also follows a normal distribution with mean 514 and standard deviation of 117. Raj took the CAT and scored 700 in the math section. Meanwhile, his friend Rahul scored 30 in the GMAT math section. Who do you think performed better? 

Find 80%, 85%, 99, 99% confidence interval for the sample mean of a population,. if we know that a random sample of 70. people from the population, the sample mean is 60 and standard deviation. is. 5

The mean dying rate of mice administered yo a given dosage of an experimental drug is 45with a variance of 25. What is the probability randomly selected 55 mice, which received the drug, more than 50 will die? Assume normality

A self-service photo centre allows you to make prints of pictures on an A4 size page. Two types of layouts

are available:

nnnnnlayout x: four pictures are fitted on one page, each has size 6 cm by 4 cm

nnnnnlayout y: two pictures are fitted on one page, each has size 15 cm by 9 cm

It costs R30 to print one page with layout x and it costs R40 to print one page with layout y.

You want at least 16 pictures of any size, and you are willing to spend up to R240. Write and graph a

system of inequalities that models the situation. Shade the solution space of the system of inequalities.

Jemima has three boxes whose total weight is 51 1

5 kg. Box B weighs 5 1

2 kg more than box A and box C

weighs 3 1

5 kg more than box B. Choose the correct statement.

[1] Box A weighs 17 5

6 kg.

[2] Box C weighs 21 1

30 kg.

[3] Box A weighs 42 1

2 kg.

[4] Box B weighs 12 1

3 kg.

The equations of three quadratic functions are given below:

(i) y = 2x2 + 12x + 18

(ii) y = −3x2 − 5x + 3

(iii) y = x2 + 2x − 5

Determine the discriminant of each function and the number of x-intercepts that the parabola has. Choose

the correct sentence. The function described in

[1] (i) has no discriminant and the parabola has no x-intercepts

[2] (ii) has a negative discriminant and the parabola has two x-intercepts

[3] (i) has a zero discriminant and the parabola has one x-intercept

[4] (iii) has a positive discriminant and the parabola has one x-intercept

A coffee shop owner blends a gourmet brand of coffee with a cheaper brand. The gourmet coffee usually

sells for R420,00 per kilogram. The cheaper brand sells for R180,00 per kilogram. How much of each type

should be mixed in order to have 30 kilograms of coffee that is worth R240,00 per kilogram?

Choose the correct sentence:

[1] Three quarters of the mass should be from the cheaper brand.

[2] He should order 7,50 kg of the cheaper brand.

[3] A third of the mass should be from the gourmet brand.

[4] He should order 6,14 kg of the gourmet brand.