at one high school, the mean time for running the 100-yard dash is 15.2 seconds with a standard deviation of 0.9 seconds. the times are very

Question

at one high school, the mean time for running the 100-yard dash is 15.2 seconds with a standard deviation of 0.9 seconds. the times are very closely approximated by a normal curve. find the percent of times that are at least 14.3 seconds

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MichaelMet 2 months 2021-08-28T18:35:38+00:00 1 Answers 0 views 0

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    2021-08-28T18:37:17+00:00

    Answer:

    The percent of times that are at least 14.3 seconds is approximately 16%.

    Step-by-step explanation:

    Let X denote the time for running the 100-yard dash.

    It is provided that the times are very closely approximated by a normal curve.

    So, the random variable X follows a normal distribution with a mean time of 15.2 seconds and with a standard deviation of 0.9 seconds.

    Compute the probability of times that are at least 14.3 seconds as follows:

    P(X\geq 14.3)=P(\frac{X-\mu}{\sigma}\geq \frac{14.3-15.2}{0.9})

                        =P(Z\geq -1)\\\\=1-P(Z<-1)\\\\=P(Z<-1)\\\\=0.15866\\\\\approx 0.159

    *Use a z-table.

    Thus, the percent of times that are at least 14.3 seconds is approximately 16%.

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