Statistics and Probability Answers

If the probability of finding working light bulbs in a factory in a warehouse that stores them is the same as our probabilities of finding working light bulbs in a box (as in our problem above), what is the (a.) expected number of light bulbs that will work given you pick out 50? (You can assume replacement/independence here because our warehouse holds thousands of light bulbs).

3.) You have a box filled with 10 light bulbs. Seven are good, three are not. You pick light bulbs at random. You do not put them back after you pick them out (without replacement). You pick two out of the box. What is the chance that:

a.) Neither is good? 

b.) Both are good?

c.) Only one is good? 

Solve for the confidence interval estimate of the population proportion.

Mikay conducted poll survey in which 520 of 1200 randomly selected voters indicated their preference for a certain candidate. What is the true population proportion of voters who prefer the candidate using 95% confidence interval?

In a normal distribution, 8% of items are under 50 and 10% are over 60. Find the mean and standard deviation of the distribution. 

A company prices its tornado insurance using the following assumptions : In any calendar year, there can be at most one tornado. In any calendar year, the probability of a tornado is 0.07. The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year . Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 20-year period

Stephen has found that the average weight packed gummy candies selected from a normally distributed population is 200g with standard deviation of 8g. Find the point and interval estimates of all gummy candies using 99% confidence level.

 In Pleasantville about 25% of the residents prefer vanilla ice cream over other flavors. A certain day, 175 residents of Pleasantville went to an ice cream store, what is the probabil- ity that 50 or more will get vanilla ice cream?

The time X a vehicle takes to go through a certain tunnel has mean μ = 12.1 minutes and standard deviation σ = 3.8 minutes. Engineers have estimated that for safety reasons, vehicles should spend on average between 11 and 13 minutes in the tunnel. Assume that there are 50 cars in the tunnel. What is the probability that the mean time X ̄ that these cars will spend on the tunnel is between 11 and 13 minutes?

Heights X of 18 years old man in U.S. are normally distributed with mean μ = 68 inches and standard deviation σ = 3 inches.

(a) What is the probability that the height of a randomly selected 18 years old man in U.S. will be less than 67 inches?

(b) Whats the probability that the mean height X ̄ of 9 randomly selected 18 years old U.S. men will be less than 67 inches?

Scores in a standardized exam are normally distributed with mean μ = 510 and standard deviation σ = 60. The middle 75% of scores are classified as “average”. Find the range of scores that are average according to this definition.