1. Measuring blood pressure is a vital process in determining a patient's immediate health condition. If the systolic blood pressure exceeds 150mm Hg, the patient is considered to have high blood pressure and medication may be prescribed. Assume that a patient's systolic blood pressure reading during a given day follows a normal distribution with a mean of 160mm Hg and a standard deviation of 20mm Hg. (a) If 5 readings are taken at various times during the day, determine the probability that the average blood pressure reading will be less than 150mm Hg and hence, fail to indicate that the patient has a high blood pressure problem. (b) Determine the number of readings required so that the probability is at most 1% of failing to detect that a patient has high blood pressure.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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