Videocassette Recorder (VCR) Tapes Are Designed So That Users Can

question 79

Essay

Videocassette recorder (VCR) tapes are designed so that users can repeatedly record new material over old material. However, after a number of re-recordings the tape begins to deteriorate. A VCR tape manufacturer is experimenting with a new technology, which hopefully will produce longer-lasting tapes. Thirty of the old-style tapes and 30 utilising the new technology were used in an experiment. The tapes were used to record and re-record programs until they began to deteriorate. The number of re-recordings is assumed to be normally distributed. It is generally accepted that the number of re-recordings should exceed 55. Any tapes that do not meet this criterion are considered to be unacceptable. The number of re-recordings were observed and shown in the accompanying table. $$\begin{array} { | c | c | c | c | c | c | } \hline { \text { Old-style tapes } } &&& { \text { New-technology tapes } } \\\hline 60 & 61 & 48 & 68 & 70 & 58 \\\hline 51 & 46 & 66 & 74 & 72 & 69 \\\hline 66 & 63 & 61 & 77 & 73 & 49 \\\hline 73 & 55 & 71 & 59 & 66 & 61 \\\hline 71 & 49 & 76 & 52 & 58 & 59 \\\hline 47 & 56 & 55 & 66 & 51 & 49 \\\hline 60 & 62 & 64 & 62 & 59 & 57 \\\hline 52 & 51 & 63 & 51 & 56 & 66 \\\hline 64 & 68 & 52 & 50 & 55 & 76 \\\hline 47 & 55 & 58 & 63 & 68 & 78 \\\hline\end{array}$$ Estimate with 90% confidence the population variance of the number of re-recordings of the new tape.

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Definitions:

Compounded Daily

A method where interest is calculated and added to the account balance every day, leading to higher yields over time.

Loan

Borrowed money that is typically repaid with interest.

Compounded Daily

The process of calculating interest where the accrued interest is added to the principal sum each day, resulting in interest earnings on interest.

Investment Account

An account held at a financial institution that is used by investors to hold and manage securities, such as stocks, bonds, and mutual funds, and other investments.