Statistics and Probability Answers

Suppose that certain bolts have length L=400+X mm, where X is a random variable with density f(x)=3/4(1-x²) if -1<=x<=1 and 0 otherwise. Determine c so that with a probability of 95% bolt will have the length between 400-c and 400+c.

Assume that the test scores from a college admissions test are normally distributed with a mean of 450 and a standard deviation of 100. 1) What percentage of people taking the test score are between 400 and 500? 2) Suppose someone received a score of 360. What percentage of the people taking the test score better? What percentage score worse? 3) If a particular university will not admit anyone scoring below 480, what percentage of the persons taking the test would be acceptable to the university?

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 178 cm178 cm and a standard deviation of 5 cm5 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values?
a. 168168 cm and 188188 cm
b. 163163 cm and 193193 cm

Find the area to the left of the curve for the following: Z=2.52

given a normal distribution with a mean of 10 and a standard deviation of 5, what is the probability that a variable is greater than 5?

the area that falls between z= -2 and Z=0 is approximately?

which distribution has the smallest spread?

A production process is considered in control if no more than 6% of the items produced are defective. Samples of size 300 are used for the inspection process.

What is the standard error of the population in this case?

What is the upper control limit?

What is the lower control limit?

During summer vacations Tanuja wants to visit three cities, Kolkata, Bhubneshvar and Chennai randomly. Find the probability that she will visit (i) Bhubaneswar before Chennai (ii) Bhubaneswar just before Kolkata.

Candidate - Rank by Prof A - Rank by Prof B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9

What is the Spearman rank-correlation coefficient (rs)?

What is σrs?

What is the value of the test statistic z?

What is the p-value?

Using α = .02 what is your conclusion about how Professor A and Professor B rank the twelve students?