Statistics and Probability Answers

Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of

μ=23.9

in. and a standard deviation of

σ=1.2

in. These data are often used in the design of different​ seats, including aircraft​ seats, train​ seats, theater​ seats, and classroom seats. Instead of using 0.05 for identifying significant​ values, use the criteria that a value x is significantly high if​ P(x or

​greater)≤0.01

and a value is significantly low if​ P(x or

​less)≤0.01.

Find the​ back-to-knee lengths separating significant values from those that are not significant. Using these​ criteria, is a​ back-to-knee length of

26.1

in. significantly​ high?

Find the​ back-to-knee lengths separating significant values from those that are not significant.

​Back-to-knee lengths greater than 

The daily income of a clerk works in a road construction sites is normally distributed with a mean of 2800 per day and a standard deviation of 300.what is the probability that a clerk of works selected at random will earn

Less than 2400 per week

Between 2500 and 3500 per week

If 2000 clerks were employed in a given day ,how many earned less than 2400 that day

Truck driver at the border tool station to be cleared at a rate of two per hour the distribution of arrivals approximates a poisson distribution

What is the probability that no truck arrives in a particular hour

What is the probability that at least one truck arrives during a particular hour

The probability of success on any trial of a binomial experiment is 25%. Find the probability that the proportion of successes in a sample of 500 is less than 22%.

Performance Task - Hypothesis Testing on Population Mean

Title: Mean Height of Local Adults

Directions: In a national survey by Food and Nutrition Research Institute of the Department of

Science and Technology on April 2014 to adult Filipinos (20 years old and older), the average

height of males is 163 cm with a standard deviation of 6 cm, and the average height of females

is 151.4 cm with a standard deviation of 5 cm. You are a local statistician and you are interested

to know if the average height of the adult males (or females) in your locality is different to the

national average height. Use the knowledge on Hypothesis Testing on Population Mean, and do

the following:

C. At 95% confidence, test the null hypothesis that there is no significant difference

between the national average height and the local average height.

An experimental study was conducted by a researcher to determine if a new time slot has an effecton the performance of pupils in mathematics. Fifteen randomly selected learners participated in thestudy. Toward the end of the investigation, a standardized assessment was conducted. The samplemean was X = 85 and the standard deviation s = 3. In the standardization of the test, the mean was75 and the standard deviation was 10. Based on the evidence at hand, is the new time slot effective?Use a = 0.05.​

 In a school, 30 percent of the students do not travel by bus. From a sample

   of 10 students find the probability that (a) at least 3 students travel by bus

   (b) at most 4 students travel by bus (c) between 2 and 7 clients students

   travel by bus