Name Directions Solve the following problems and answer the

Name: Directions: Solve the following problems and answer the following questions. Then, report the most appropriate response in the corresponding online test feature. Special Note: Keep your software solutions because you will be able to submit them separately as another assessment. For Problems #1 through tia, consider the following context: According to a medical research study, the population of adult patients with first stage high blood pressure is normally distributed with a population mean of 150 mm Hg and a population standard deviation of 5 mm Hg for systolic blood pressure measurements. A patient from the population with first stage high blood pressure is then randomly selected. [COMMENTS & HINTS: If it applies, please do not simply state the answer using the Empirical Rule generalities. Do the more precise computations. Repeat, please be precise in your approximations! Utilize the final answer rounded to four decimal places 0 and then express it as a percentage as follows: or Ex: Express 0.8765 as 87.65% or 0.0123 as 1.23% #1: What is the chance the patient\'s blood pressure is reported between i45 mm Hg and 155 Hg? #2: What is the chance the patient\'s blood pressure is reported between 140 mm Hg and 160 mm Hg? #3 What is the chance the patient\'s blood pressure is reported between 135 mm Hg and 165 mm Hg? #4: What is the chance the patient\'s blood pressure is reported as greater than 148 mm Hg? #5: what is the chance the patient\'s blood pressure is reporte as no more than i48 mm Hg? #6 What is the chance the patient\'s blood pressure is reported between 147 mm Hg and 157 Hg? #7 What is the chance the patient\'s blood pressure is reporte between 141 mm Hg and 149mm Hg? #8 What is the chance the patient\'s blood pressure is reported between 151 mm Hg and mm Hg? #9: What is the chance the patient\'s blood pressure is reported between 143 mm Hg and 145mm Hg #10: What is the chance the patient\'s blood pressure is reported between 155 mm Hg and 157mm Hg

Solution

Mean = u = 150
SD = 5

1)

z = (x - u) / SD
z = (145 - 150)/5 = -1
P(z < -1) = 0.1587

z = (x - u)/SD
z = (155-150)/5 = 1
P(z < 1) = 0.8413

So, P(-1 < z < 1) = 0.8413 - 0.1587

0.6826

68.26%

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2)

For x = 140, z = -2
P(z < -2) = 0.0228

For x = 160, z = 2
P(z < 2) = 0.9772

So, 0.9772 - 0.0228

0.9544

95.44%

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3)

For x = 135, z = -3
P(z < -3) = 0.0013

For x = 165, z = 3
P(z < 3) = 0.9987

0.9987 - 0.0013

0.9974

99.74%

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4)

x = 148

z = (x - u) / SD
z = (148 - 150)/5
z = -2/5
z = -0.4

Use this link ---> https://www.easycalculation.com/statistics/p-value-for-z-score.php

P(z > -0.4) = 0.6554 = 65.54% --> ANSWER

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5) P(x <= 148) = 1 - 0.6554

0.3446 = 34.46% --> ANSWER

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6) Between 147 and 157 :

z = (147 - 150) / 5 = -0.6
P(z < -0.6) = 0.2743

z = (157 - 150) / 5 = 1.4
P(z < 1.4) = 0.9192

0.9192 - 0.2743

0.6449

64.49% --> ANSWER

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7)

z = (141 - 150) / 5
z = -1.8
P(z < -1.8) = 0.0359

z = (149 - 150) / 5
z = -0.2
P(z < -0.2) = 0.4207

0.4207 - 0.0359

0.3848

38.48% --> ANSWER

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8)

z = (151 - 150)/5 = 0.2
P(z < 0.2) = 0.5793

z = (159 - 150)/5 = 1.8
P(z < 1.8) = 0.9641

0.9641 - 0.5793

0.3848

38.48%

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9)

z = (143 - 150) / 5 = -1.4
P(z < -1.4) = 0.0808

z = (145 - 150) / 5 = -1
P(z < -1) = 0.1587

0.1587 - 0.0808

0.0779

7.79%

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10)

z = (155 - 150) / 5
z = 1
P(z < 1) = 0.8413

z = (157 - 150) / 5
z = 1.4
P(z < 1.4) = 0.9192

0.9192 - 0.8413

0.0779

7.79%