An experiment was conducted to estimate the strength of certain kind of braided cord after weathering. The strengths of 56 pieces of cord that had been weathered for 30 days were investigated. The 56 pieces of cord were placed simultaneously in a tensile strength device. The device applies an increasing amount of force until the cord fails.
These are the cord strengths:
19.7 21.6 21.9 23.5 24.2 24.4 24.9 25.1
26.4 26.9 27.6 27.7 27.9 28.4 29.8 30.7
31.1 31.1 31.7 31.8 32.6 34.0 34.8 34.9
35.1 36.6 37.0 37.7 38.7 38.7 39.0 39.6
40.0 41.4 41.4 41.8 42.2 43.5 44.5 45.0
45.5 45.9 46.3 46.7 46.7 47.0 47.0 47.4
47.6 48.6 48.8 57.9 58.3 67.9 84.2 97.3
Question:
The manufacturer of the cords would like to estimate the proportion of weathered cords having tensile strength less than 50 psi. Provide a 95% confidence interval based on the information from the failure data from the 56 cords.