Statistics and Probability Answers

Replacement times of TV sets are reported to follow a normal distribution having a mean

of 8.5 years with standard deviation of 1.2 years.

a. If 30 TV sets are selected at random, what is the probability that the mean

replacement time is less than 8 years?

b. If 20 TV sets are selected, what is the probability that the mean replacement

time is longer than 7.8 years?

c. If 25 TV sets are randomly selected, what is the probability that the

replacement time is between 8.4 years and 9 years?

The mean NAT scores of Grade 10 students is 65. Sixty (60) students were chosen and

found that the standard deviation of their scores is 5. What is the probability that their

mean is between 64 and 67?

The mean NAT scores of Grade 10 students is 65. Sixty (60) students were chosen and

found that the standard deviation of their scores is 5. What is the probability that their

mean is between 64 and 67?

The Smith Trucking Company claims that the average weight of its delivery trucks when fully loaded is 6000 pounds with a standard deviation of 120 pounds. 36 trucks are selected at random and their weights recorded. Within what limits will the average weights of 90% of the 36 trucks lie?

A box contains 6 defective bulbs and 10 functional bulbs. If 4 bulbs are to be chosen at random. what is the probability that there are 2 defective bulbs and 2 functional bulbs selected?

A study reports that 5% of adults are afraid to be home alone at night. If 20 people are randomly selected, what is the probability at least 3 of them are afraid to be home alone at night?

A Random sample of 60 grade 11 students ages is obtained to estimate the mean ages of all grade 11 students. Suppose the sample mean is 17.3 and the population variance is 18,

1. What is the point of estimate of the population parameter?

2.Find the 95% confidence interval for the population parameter?

3.Find the 99% confidence interval for the population parameter?

A company has developed a new battery. The engineering department of the company claims that each battery lasts for 200 minutes. In order to test this claim, the company selects a random sample of 100 new batteries so that this sample has a mean of 190 minutes. Given that the population standard deviation is 30 minutes, test the engineering department’s claim that the new batteries run with an average of 200 minutes. Use 1% level of significance.

Which is the correct null hypothesis that can be derived in the situation?

Which is the correct alternative hypothesis that can be derived in the situation? 

What test will be used based from the given values in the situation? 

What is the decision based from the critical value and the computed test statistic?

In an advertisement, a certain brand of shampoo is claiming that

the use of this product will make the hair grow faster. It is known

that the mean length of growing hair over thirty days is 2 cm. What would be its H₀ and H₁?

The federation of private school teachers has developed a

new evaluation instrument that they claim has higher

reliability by producing less error in evaluation. In the past, the

mean number of errors in the evaluation was 20%. What would be its H₀ and H₁?