Statistics and Probability Answers

All sections of an Introduction to Criminology course at a large university were given the same final exam. Test scores were distributed normally with a mean of 68 and a standard deviation of 6.
a) What percentage of students scored between 60 and 69 (a grade of C) and what percentage scored between 70 and 79 (a grade of B)?
b) In words, briefly summarize your findings.

A batch of 10 products comes randomly from three factories A, B and C. This batch is checked to detect the defective products. The defective rates of three factories A, B and C are 5%, 10% and 15% respectively
a. Determine the probability that there are exactly two defective products
b. Given that this batch has two defectives, what is the probability that it comes from factory B
c. If there are two batches come from the same factory and first one has exactly two defective items, what is the probability that the second one has two defectives?

Test the hypothesis that the average dissolution time is 20 seconds, using the random sample of dissolution times below.
Dissolution time (secs): 23 19 26 22 18 27

(b) Two different instruments were used to make a number of replicate measurements. The results were:
Instrument A: 12.06 12.14 12.03 12.09 12.05
Instrument B: 14.62 14.97 14.60 14.51 14.01 14.11
Do these results indicate that either instrument is more precise?

two cards are drawn successively without replacement from a shuffled deck of cards. make a probability distribution table where random variable x represents the number of heart

Suppose a special type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The p.d.f that characterizes the proportion Y that make a profit is given by: ky^4(1-y)^3 and 0 elsewhere.
A. What is the value of k that renders the above a valid density function?
B.Find the probability that at most 50% of the firms make a profit in the first year.
C. Find the probability that at least 80% of the firms make a profit in the first year.

consider the sampling distribution of x for random samples of 65 customers satisfactons ratings.Determine the probability of observing a sample mean greater than or equal to 42.95 when we assume that mean equals 42.

Supposing that the length of certain machine parts may be looked upon as a random variable having a normal distribution with a mean of 2.000 cm, and a standard deviation of 0.050 cm. specifically we want to test the null hypothesis µ = 2.000 against alternative hypothesis µ not equal to 2.000, on the basis of mean of a random sample of size 30. If probability of type 1 error is 0.05 what is the probability of type 2 error for µ=2.010?

An experiment has 8 possible​ outcomes, all equally likely. An event can occur in 4 ways. Find the probability that the event occurs.
The probability that the event occurs is

Table 1: Score
27 37 30 28 39 25 45 28
32 28 26 38 31 30 47 41

Based on Table 1, organize the data into a frequency distribution by taking 25 as the lowest boundary and 5 as the class width.

Construct a “less than or equal” ogive for the frequency distribution established in (a) and then approximate the number of candidates who scores below 35.

A website has on the average two hits per hour. Assuming a Poisson distribution for the number of hits per hour (X), calculate the probability that there are at most three hits.