Question

For each probability and percentile problem, draw the picture The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from 5.6 to 6.6 years. We randomly select one first grader from the class. E Part (a) In words, define the random variable X. O the age of elementary school children on September 1 the age of a first grader on September 1 the age of a first grader on the first day of school the number of children in first grade E Part (b) Give the distribution of Part (c) E Part (d Enter an exact number as an integer, fraction, or decimal. f(x) where S x S E Part (e) Enter your answer to one decimal place

Answer 1

The random variable X represents the age of a first grader on September 1 and follows a uniform distribution. The probability distribution for X and the probabilities of specific age ranges can be calculated using uniform distribution formulas, including finding percentile values.

Step-by-step explanation:

The student's question involves understanding and working with a probability distribution model known as the uniform distribution. This model is used when a variable is equally likely to fall anywhere within a certain range. Specifically, the student question refers to the age of first graders being uniformly distributed between 5.8 and 6.8 years old. Part (a) of the question asks to define the random variable X. Here, X would represent the age of a first grader on September 1. Since this is a uniform distribution, the probability density function, f(x), can be found by taking 1 divided by the difference between the maximum and minimum values of the range.

In part (b), the distribution of X would be uniform, and we denote this by writing X~Uniform(a, b), where 'a' and 'b' represent the lower and upper bounds of the ages, respectively. The values of 'a' and 'b' would be 5.8 and 6.8 in this case. The calculation of probabilities for specific age ranges, such as being over 6.5 years old, would involve finding the area under the curve of the density function for the specified range. For a theoretical percentile, such as the 70th percentile, you would look at the cumulative distribution function and find the age x such that P(X < x) = 0.70.