Human body temperatures have a mean of 98.20° F and a standard deviation of 0.62°. Sally's temperature can be described by z = -1.5. What is her temperature? Round your answer to the nearest hundredth.

Answers

Answer 1

Answer:

Answer:

$97.27^(o)F$

Step-by-step explanation:

We have been given that human body temperatures have a mean of 98.20° F and a standard deviation of 0.62°. Sally's temperature can be described by z = -1.5.

To find Sally's temperature we will use z-score formula.

$z=(x-\mu)/(\sigma)$ , where $\mu$ = Mean, $\sigma$ = Standard deviation.

Let us substitute our given values in z-score formula.

$-1.5=(x-98.20)/(0.62)$

Multiply 0.62 to both sides of equation.

$0.62*-1.5=0.62* (x-98.20)/(0.62)$

$-0.93=x-98.20$

Add 98.20 to both sides of equation.

$-0.93+98.20=x-98.20+98.20$

$97.27=x$

Therefore, Sally's temperature will be 97.27 degrees Fahrenheit.

Answer 2

Answer: $Z=\frac{X-\mu}\sigma\iff-1.5=(X-98.20^\circ)/(0.62^\circ)\implies X\approx97.27^\circ$

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Scores on a recent national statistics exam were normally distributed with a mean of 82.2 and a standard deviation of 5.If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award

Answers

Answer:

The lowest score eligible for an award is 92.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

$\mu = 82.2, \sigma = 5$

If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award

The lowest score is the 100 - 2.5 = 97.5th percentile, which is X when Z has a pvalue of 0.975. So X when Z = 1.96. Then

$Z = (X - \mu)/(\sigma)$

$1.96 = (X - 82.2)/(5)$

$X - 82.2 = 5*1.96$

$X = 92$

The lowest score eligible for an award is 92.

What is the number if 2 is 12.5% of a number?
PLS HELP ME!!!

Answers

16 since 12.5% is 1/8 of 100 and 2 times 8 is 16

The answer to the question is 25.

At $ 0.49 per bushel, the daily supply for wheat is 409 bushels, and the daily demand is 589 bushels. When the price is raised to $ 0.85 per bushel, the daily supply increases to 529 bushels, and the daily demand decreases to 229 bushels. Assume that the price-supply and price-demand equations are linear.(A) Find the supply equation.
(B) Find the demand equation.
(C) Find the equilibrium price and quantity

Answers

Answer:

(A) Find the supply equation.

Qs = 245.67 + 333.33Ps

(B) Find the demand equation.

Qd = 1079 - 1000Pd

Price P = $0.625

Quantity Q = 454 bushels

Step-by-step explanation:

The demand equation is of the form;

Q = a - bP

The supply equation is of the form;

Q = c + eP

We need to determine the values of a,b,c,d;

At $ 0.49 per bushel, the daily supply for wheat is 409 bushels, and the daily demand is 589 bushels

589 = a - b(0.49) ........1

409 = c + e(0.49) .........2

When the price is raised to $ 0.85 per bushel, the daily supply increases to 529 bushels, and the daily demand decreases to 229 bushels;

229 = a - b(0.85) ........3

529 = c + e(0.85). .......4

Subtract equation 3 from 1

589-229 = b(0.85) - b(0.49)

360 = b(0.36)

b = 360÷0.36

b = 1000

Using equation 1

589 = a - 1000(0.49)

a = 589+490 = 1079

Subtract equation 2 from 4

529-409= e(0.85) - e(0.49)

120 = 0.36e

e = 120/0.36

e = 333.33

Using equation 2

409 = c + 333.33(0.49)

c = 409 - 333.33(0.49)

c = 245.67

Therefore the demand equation is;

Qd = 1079 - 1000Pd

The supply equation is ;

Qs = 245.67 + 333.33Ps

The equilibrium price is at Qs = Qd and Ps = Pd

1079-1000P = 245.67 +333.33P

P = (1079-245.67)/(1000+333.33)

P = $0.625

Qd = 1079 - 1000(0.625)

Qs = Qd = 454

Find the area of the circle. Use 3.14 for pi.Question 1 options:

113.04 in2

56.52 in2

256.34 in2

1017.36 in2

Answers

Answer:

The answer is 254.34in².

Step-by-step explanation:

Given that the diameter is 2 times the radius. So the radius will be 9 in. Next, you have to find the area of circle, A = π × r² :

A = π × r²

Let π = 3.14, r = 9,

A = 3.14 × 9²

A = 254.34 in²

Find three consecutive integers whose sum is 216. (Hint: if n represents the smallest of the three integers, n + 1 and n + 2 representthe other two numbers.)