Statistics and Probability Answers

Suppose the mean amount of cholesterol in eggs labeled “large” is 186 milligrams, with standard deviation 7 milligrams. Find the probability that the mean amount of cholesterol in a sample of 144 eggs will be within 1.5 milligrams of the population mean.

Samples of two cards are drawn at random from a population of 6 cards numbered from 1 to 6.

A. How many possible samples can be drawn?

B. Construct the sampling distribution of sample means.

Directions: Read and analyze the given problems below. Write your solutions and final answer on a separate sheet of paper. 1. ILAW Manufacturing company produces bulbs that last a mean of 900 hours with a standard deviation of 110 What is the probability that the mean lifetime of a random sample of 15 of these bulbs is less than 850 hours?

SOLUTION:

A sample of 60 Grade 9 students' ages was obtained to estimate the mean age of all Grade 9 students.

X = 15.3 years and the population variance is 16.

a. What is the point estimate for u.?

b. Find the 95% confidence interval for u?

c. Find the 99% confidence interval for u?

The weights of students in a certain school are normally distributed with a mean weight of 66 kg. 10% have a weight greater than 70kg. What percentage of students weighs between 52kg and 66kg?   

1. A DepEd official claim that the average performance in Mathematics is 82.4%. A random of 25 students showed that their mean performance in Mathematics is 81.3% with a standard deviation of 4.2%. Test whether the mean performance of the students is not significantly lower than the general average. Use 0.01 level of significance.

Two dices are tossed together, what is the probability of having a multiple of 12.

2. In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability

that a score picked at random will lie

ve score 50?

b. below score 38?

a.

3.

Consider the normal distribution of IQs with a mean of 100 and a standard dev

n = 68, ¯x=75, and σ = 8. The sample population is normally distributed. Find the 99% interval estimate for µ.

A sample of 100 Grade 9 students’ ages have been obtained to estimate the mean age of all Grade 9 students. ¯x=16 years and the population variance is 0.75 years. Find the 95% confidence interval for µ.