An experiment was conducted to find out the strength of a certain kind of braided cord after weathering. The strengths of 56 pieces of cord which had been weathered for 30 days were investigated. The 56 pieces of cord were placed concurrently in tensile strength device. The device applies a rising amount of force till 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 determine the proportion of weathered cords having tensile strength less than 50 psi. Give a 95% confidence interval based upon the information from the failure data from the 56 cords.