Hw7_24

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Statistics

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Jul 2, 2024

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1 NAME: STAT:1010 Statistics and Society Instructor: Osnat Stramer HOMEWORK 7 Submit your work as a single file to Canvas/ICON. Please check that your work is readable. 1. Among females in the US, diastolic blood pressures, are normally distributed with mean µ=77 mm Hg and standard deviation ࠵? =3 mm. According to the empirical rule, what percentage of women have a diastolic blood pressure higher than 80 mm Hg? a. 2.5% b. 16% c. 68% d. 95% e. 97.5% 2. In reference to question 1, what is the 1.5 th percentile of the blood pressures? The z-Score for the 1.5 th percentile is z= -2.17009 a. 70.49 b. 83.51 c. 74.22 d. 82.11 e. None of the above 3. The annual precipitation amounts are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood (proportion) that the annual precipitation is bigger than 90.8? a. 0.6103 b. 0.3897 c. 0.0250 d. 0.2200 4. In reference to question 3, what is the likelihood (proportion) that the mean annual precipitation during 25 randomly picked years will be less than 90.8? a. 0.6103 b. 0.3897 c. 0.0808 d. 0.9192 e. 0.5808

2 5. The `length of stay' for individuals at a hospital has a distribution with a mean of 17 days and a standard deviation of 3 days. A random sample of 36 patients is chosen. What is the probability that the average `length of stay' for the sample is more than 18.25 days? a. 0.0062 b. 0.3372 c. 0.9938 d. 0.6628 e. 0.0001 6. The green turtle migrates across the Southern Atlantic in the winter, swimming great distances. A study found that the mean migration distance was 2,200 kilometers and the standard deviation was 625 kilometers. Assume that the distances are normally distributed. a. Find the probability that a single randomly selected green turtle migrates less than 1,900 kilometers (this is the same as the percent of all green turtles that migrate less than 1,900 kilometers). b. Find the probability that a single randomly selected green turtle migrates between 2,000 kilometers and 2,500 kilometers. 7. In reference to question 6, a multiple samples of migration distances for 32 green turtles are randomly selected and the mean migration distance is found for each sample. a. What is the shape of the distribution of the sample means? b. What is the mean of the sample means? c. What is the standard deviation of the sample means? d. Find the probability that the sample mean of the distance migrated by the 32 turtles is less than 1,900 kilometers (this is the same as the percent of all sample means of size 32 that migrate less than 1,900 kilometers). 8. The following data describe the diameter (in inches) of four rods: 14, 16, 13, 14. Calculate the standard deviation. (a) 2.00 (b) 1.58 (c) 1.26 (d) 1.12 (e) 1.09

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