Math Answers

The amount of time a student taking statistics spends on studying for a test is normally distributed. If the average time spent studying is 10 hours and the standard deviation is 4

hours,

a. What is the probability that a student will spend more than 13 hours studying?

b. What is the probability that a student will spend between 9 to 11 hours studying?

c. What is the probability that a student will spend less than 8 hours studying?

A normally distributed population has a mean of 25.6 and a standard deviation of 3.3. Find the probability that a single randomly selected element X of the population exceeds 30.

The factory owner claimed that their bottled fruit juice has the capacity of less than an average of 280ml. To test the claim, a group of consumers gets a sample of 80 bottles of the fruit juice, calculates the capacity, and then finds the mean capacity to be 265ml. The standard deviation is 8ml. Use a= 0.05 level of significance to test the claim.

Suppose that the lifetimes of electric light bulbs follow an Exponential distribution with mean

1000 hours. A

random sample of 40 light bulbs is tested. The probability that the mean

lifetime is at least 900 hours is:

There are 10 girls and 7 boys in a class and need to select 4 students as a school representative. In how many ways can we select of 2 girls and 2 boys?

A store contains 1 pair of boots with each of the following colors are black, chocolate and yellow. Each pair is put together in a particular place. You enter into the dark store and pick randomly the boot without looking at it. Then, you replace it with another boots. What is the probability that you will choose the black pair of boots both times?

5. A coin is tossed 400 times. Use the normal curve approximation to find the probability of obtaining

(a) between 185 and 210 heads inclusive;

(b) exactly 205 heads;

(c) fewer than 176 or more than 227 heads

How many strings can be formed in the length of 5 strings from the word DISCRETE?

4. The heights of 1000 students are normally distributed with a mean of 175 centimeters and a standard deviation of 7 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would you expect to have heights

(a) less than 160.0 centimeters?

(b) between 171.5 and 182.0 centimeters inclusive?

(c) equal to 175.0 centimeters?

(d) greater than or equal to 188.0 centimeters?

Evalu‎ate ∫_C (x + 2y) ds, w‎here C is the cu‎rve defi‎ned by y = √(4 − x²), for x ∈ [0, 1].