Statistics and Probability Answers

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

In a medical study, patients are classified in 8 ways according to whether they have

blood type AB+, AB−, A+, A−, B+, B− , O+, or O−, and also according to whether their

blood pressure is low, normal, or high. Find the number of ways in which a patient can

be classified.

Find the value of σ x̅. Use the choices on no. 4 problem. Use this data: Consider the score examples illustrated, in which random samples of size 16 are obtained from N (25,9)

Two of the five (5) foreign automobiles from an overseas shipment have slight paint blemishes. If an

agency receives three (3) of these automobiles at random, list the elements of the sample space 𝑆 using

the letters B and N for “blemished” and “non-blemished”, respectively. For each sample point, assign a

value 𝑥 of the random variable 𝑋 representing the number of automobiles purchased by the agency with

paint blemishes. Hint: There are eight (8) elements in the sample space.

What is the value of σ2 x̅? Use this data: Consider the score examples illustrated, in which random samples of size 16 are obtained from N (25,9)

Consider the score examples illustrated, in which random samples of size 16 are obtained from N (25,9). What is the value of μ x̅

An overseas shipment of 5 foreign automobiles contains 2 that have slight paint

blemishes. If an agency receives 3 of these automobiles at random, find the

probability distribution of the random variable X representing the number of

automobiles with paint blemishes purchased by the agency. Find the mean

number of automobiles with paint blemishes. Also, calculate the variation.

There are 4 boys and 2 girls in room A and 5 boys and 3 girls in room B .A girl from one of the two rooms laughed loudly.what is the probability that the girl who laughed was from room B?