Normal Distribution Estimation Worksheets Grade 11

1. A city planner is analyzing traffic flow data and finds that the number of cars passing through an intersection follows a sinusoidal pattern throughout the day. The function modeling this is f(t) = 250sin(π/12(t - 6)) + 350, where t is the time in hours after midnight. During what time intervals is the traffic flow above 500 cars per hour?
2. A pharmaceutical company is testing a new medication and wants to estimate what percentage of patients will experience a specific side effect. In a clinical trial with 320 randomly selected patients, 24% reported experiencing the side effect. Construct a 90% confidence interval for the true population proportion of patients who would experience this side effect. (Use z* = 1.645 for the critical value)
3. Charlotte's reaction times are normally distributed with μ=272 ms and σ=17 ms. Estimate the percentage of reaction times between 238 ms and 306 ms.

…and 4 more problems

1. Isabella's reaction times are normally distributed with μ=220 milliseconds and σ=25 milliseconds. Estimate the percentage of reaction times that are greater than 270 milliseconds.
2. Liam's reaction times are normally distributed with μ = 240 ms and σ = 30 ms. Estimate the percentage of reaction times greater than 270 ms.
3. SAT scores are normally distributed with μ=1061 and σ=116. Estimate the percentage of students scoring between 945 and 1177.

…and 5 more problems

1. Sophia's reaction times are normally distributed with μ=220 milliseconds and σ=25 milliseconds. Estimate the percentage of reaction times greater than 270 milliseconds.
2. Isabella's test scores are normally distributed with μ=88 and σ=12. What percentage of students scored between 76 and 100?
3. A city is planning a new public transit system and needs to estimate what percentage of residents would use it regularly. They survey 400 randomly selected residents and find that 68% express interest. Construct a 95% confidence interval for the true population proportion of residents who would use the transit system regularly. (Use z* = 1.96 for the critical value)

…and 5 more problems