**Text Description:**Suppose $ x $ has a distribution with a mean of 80 and a standard deviation of 15. Random samples of size $ n = 36 $ are drawn.**(a)** Describe the $ \bar{x} $ distribution and compute the mean and standard deviation of the distribution.\[ \bar{x} \text{ has } \]\[ \text{an approximately normal} \]distribution with mean $ \mu_{\bar{x}} = \underline{\hspace{2cm}} $ and standard deviation $ \sigma_{\bar{x}} = \underline{\hspace{2cm}} $.**(b)** Find the $ z $ value corresponding to $ \bar{x} = 82.5 $.\[ z = \underline{\hspace{4cm}} \]**(c)** Find $ P(\bar{x} < 82.5) $. (Round your answer to four decimal places.)\[ P(\bar{x} < 82.5) = \underline{\hspace{4cm}} \]

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Scores on a dental anxiety scale range from 0 (no anxiety) to 20 (extreme anxiety). The scores are normally distributed with a mean of 11 and a standard deviation of 4. Find the z-score for the given score on this dental anxiety scale. 16 Z16 (Type an integer or a decimal.)
In each part, use the information given to calculate the standard error of the mean. (Round your answers to one decimal place.) (a) Mean height for a sample of n = 99 women is x = 63.4 inches, and the standard deviation is s = 2.3 inches. inches (b) Mean systolic blood pressure for a sample of n = 120 men is x = 119, and the standard deviation is s = 8. (c) Mean systolic blood pressure for a sample of n = 360 men is x = 119, and the standard deviation is s = 8.
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. (a) Find the z-score for an IQ of 119, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 119. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z- score. Use your z-score from part (a), rounded to one decimal place). Shade: Left of a value . Click and drag the arrows to adjust the values. -4 -2 -1 2 3 4 -1.5 (d) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization.
Today, the waves are crashing onto the beach every 4.5 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.5 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that wave will crash onto the beach exactly 1.7 seconds after the person arrives is P(x = 1.7) = d. The probability that the wave will crash onto the beach between 1.5 and 3.9 seconds after the person arrives is P(1.5 1) = f. Find the maximum for the lower quartile. seconds.
In each part, use the information given to calculate the standard error of the mean. (Round your answers to one decimal place.) (a) Mean height for a sample of n = 99 women is x = 65.6 inches, and the standard deviation is s = 3.9 inches.inches(b) Mean systolic blood pressure for a sample of n = 120 men is x = 124.5, and the standard deviation is s = 7.(c) Mean systolic blood pressure for a sample of n = 360 men is x = 124.5, and the standard deviation is s = 7.
Current Attempt in Progress Let x have a normal distribution with a mean of 57.7 and a standard deviation of 4.95. The z value for x = 43.38, rounded to two decimal places, is: i
Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 5.4 and standard deviation ? = 0.6. a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.) _______ < z b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.) z < ______ c) Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.) ________ < z < _______
Assume x is normally distributed with a mean of 2 and a standard deviation of 2. Find: a.P(X=2) b.P(X<2) c.P(X>=2) d.P(2 < X < 4)
The table below shows the summary statistics of the sales ($) made by company ABC in 2022. No. of month 12 134,562 135,000 48,997 95,000 185,000 90,000 Mean Median S.D Minimum Maximum Range The monthly profit should be adjusted by multiplying 0.88 then subtracting $30,000. Without calculating the profit for each month, find the new standard deviation of profit for 2022? (2 d.p.)
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. (a) Find the z-score for an IQ of 99, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 99. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x- axis is the z-score. Use your z-score from part (a), rounded to one decimal place). Shade: Left of a value -1 -1.5 0 +). Click and drag the arrows to adjust the values. 1 2 (d) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. (e) Sketch the graph, and write the probability statement. Edit Insert Formats B I U x₂ x² A => EM e & N 18 (f) The middle 50% of IQs fall between what two values? (g) Sketch the graph and write the probability statement. Edit Insert Formats BIUX₂ X² A E = = E EC P R N • Σ+ Σ Α Σ+ Σ Α

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