# Question

Children who develop unexpected difficulties with the spoken language are often diagnosed as specifically language impaired (SLI). A study published in the Journal of Speech, Language, and Hearing Research (Dec. 1997) investigated the incidence of SLI in kindergarten children. As an initial screen, each in a national sample of over 7,000 children was given a test for language performance. The percentages of children who passed and failed the screen were 73.8% and 26.2%, respectively. All children who failed the screen were tested clinically for SLI. About one-third of those who passed the screen were randomly selected and also tested for SLI. The percentage of children diagnosed with SLI in the "failed screen" group was 20.5%; the percentage diagnosed with SLI in the "pass screen" group was 2.8%.

a. For this problem, let "pass" represent a child who passed the language performance screen, "fail" represent a child who failed the screen, and "SLI" represent a child diagnosed with SLI. Now find each of the following probabilities: P(Pass), P(Fail), P(SLI | Pass), and P(SLI | Fail).

b. Use the probabilities from part a to find P(Pass ∩ SLI) and P(Fail ∩ SLI). What probability law did you use to calculate these probabilities?

c. Use the probabilities from part b to find P(SLI). What probability law did you use to calculate this probability?

a. For this problem, let "pass" represent a child who passed the language performance screen, "fail" represent a child who failed the screen, and "SLI" represent a child diagnosed with SLI. Now find each of the following probabilities: P(Pass), P(Fail), P(SLI | Pass), and P(SLI | Fail).

b. Use the probabilities from part a to find P(Pass ∩ SLI) and P(Fail ∩ SLI). What probability law did you use to calculate these probabilities?

c. Use the probabilities from part b to find P(SLI). What probability law did you use to calculate this probability?

## Answer to relevant Questions

A version of the dice game "craps" is played in the following manner. A player starts by rolling two balanced dice. If the roll (the sum of the two numbers showing on the dice) results in a 7 or 11, the player wins. If the ...According to a nationwide survey, 60% of parents with young children condone spanking their child as a regular form of punishment (Tampa Tribune, Oct. 5, 2000). Consider a random sample of three people, each of whom is a ...The degree to which democratic and nondemocratic countries attempt to control the news media was examined in the Journal of Peace Research (Nov. 1997). The article reported that 80% of all democratic regimes allow a free ...Explain why each of the following is or is not a valid probability distribution for a discrete random variable x: a. b. c. d. Consider the probability distribution shown here: a. Calculate μ, σ2, and σ. b. Graph p(x). Locate μ, μ – 2σ, and μ + 2σ on the graph. c. What is the probability that x will fall into the interval μ ± 2σ?Post your question

0