Rotation speed of a shaft can be measured by tachometers. In this method, a tachometer needs...

 

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Rotation speed of a shaft can be measured by tachometers. In this method, a tachometer needs to be slightly pressed against the end of the shaft axis to achieve synchronized rotation (otherwise there will be a slip between the two rotations). However, this method may lead to measurement errors due to either by over-pressing (extra- loading onto the shaft) or by loosely touch (slip). A set of data is given in the following table (a total of 90 measurements). Determine: a) Any bad data (assuming a confidence level of 95%)? b) The mean and standard deviation of the rotation speed (after removal of bad data); c) Plot the probability density function (pdf) distribution; d) By comparing your pdf against the corresponding Gaussian pdf, comment on the possibility and nature of a biased error in this set of measurements. Table 1 Original Measurements of Tachometer (rpm) 1906 1966 1968 1970 1905 1969 1948 1968 1970 1970 1947 1971 1942 1968 1968 1970 1941 1969 1950 1968 1966 1970 1949 1967 1952 1968 1968 1970 1951 1969 1960 1970 1966 1968 1959 1967 1964 1968 1966 1966 1963 1967 1966 1968 1968 1972 1965 1969 1966 1968 1968 1972 1965 1969 1964 1966 1966 1968 1963 1967 1960 1968 1970 1970 1959 1971 1960 1968 1970 1970 1959 1971 1964 1968 1968 1972 1963 1969 1964 1966 1970 1974 1963 1971 1966 1968 1972 1972 1965 1973 Rotation speed of a shaft can be measured by tachometers. In this method, a tachometer needs to be slightly pressed against the end of the shaft axis to achieve synchronized rotation (otherwise there will be a slip between the two rotations). However, this method may lead to measurement errors due to either by over-pressing (extra- loading onto the shaft) or by loosely touch (slip). A set of data is given in the following table (a total of 90 measurements). Determine: a) Any bad data (assuming a confidence level of 95%)? b) The mean and standard deviation of the rotation speed (after removal of bad data); c) Plot the probability density function (pdf) distribution; d) By comparing your pdf against the corresponding Gaussian pdf, comment on the possibility and nature of a biased error in this set of measurements. Table 1 Original Measurements of Tachometer (rpm) 1906 1966 1968 1970 1905 1969 1948 1968 1970 1970 1947 1971 1942 1968 1968 1970 1941 1969 1950 1968 1966 1970 1949 1967 1952 1968 1968 1970 1951 1969 1960 1970 1966 1968 1959 1967 1964 1968 1966 1966 1963 1967 1966 1968 1968 1972 1965 1969 1966 1968 1968 1972 1965 1969 1964 1966 1966 1968 1963 1967 1960 1968 1970 1970 1959 1971 1960 1968 1970 1970 1959 1971 1964 1968 1968 1972 1963 1969 1964 1966 1970 1974 1963 1971 1966 1968 1972 1972 1965 1973