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MariettaO [177]
3 years ago
6

If the heights of 300 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many studen

ts have heights (a) greater than 72 inches, (b) less than or equal to 64 inches, (c) between 65 and 71 inches inclusive, (d) equal to 68 inches? assume the measurements to be recorded to the nearest inch.
Mathematics
1 answer:
Lunna [17]3 years ago
3 0
Given:
μ = 68 in, population mean
σ = 3 in, population standard deviation

Calculate z-scores for the following random variable and determine their probabilities from standard tables.

x = 72 in:
z = (x-μ)/σ = (72-68)/3 = 1.333
P(x) = 0.9088

x = 64 in:
z = (64 -38)/3 = -1.333
P(x) = 0.0912

x = 65 in
z = (65 - 68)/3 = -1
P(x) = 0.1587

x = 71:
z = (71-68)/3 = 1
P(x) = 0.8413

Part (a)
For x > 72 in, obtain
300 - 300*0.9088 = 27.36

Answer: 27

Part (b)
For x ≤ 64 in, obtain
300*0.0912 = 27.36

Answer: 27

Part (c)
For 65 ≤ x ≤ 71, obtain
300*(0.8413 - 0.1587) = 204.78

Answer: 204

Part (d)
For x = 68 in, obtain
z = 0
P(x) = 0.5
The number of students is
300*0.5 = 150

Answer: 150

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A photography studio charges $50 that includes a sitting fee and 6 prints. Luigi increased his order to 11 prints and paid $65.
Effectus [21]

Answer:

Sitting fee - 32$

Step-by-step explanation:

This is a system of equations(let x represent the sitting fee)

x+6y=50

x+11y=65

You want to isolate the x variable - x+6y-6y=50-6y ; x = 50-6y

Input this into the 2nd equation: 50-6y+11y=65 ; 50+5y=65

Subtract 50 from both sides. 5y=15 (Divided 5y on both sides) ; y=3

Now that y = 3 input this into any equation I choose the 1st one.

x+6(3) = 50 ; x + 18 = 50 (Subtract 18 on both sides to get x)

x = 32

Prove: 32 + 6(3) = 50 ; 32+18 = 50 ; 50 = 50 True



7 0
3 years ago
Honestly, I'm trying my best to solve this but my Math XL is being so rude. ​
Valentin [98]
<h3>Answer:  19</h3>

==============================================================

Explanation:

T is the midpoint of PQ, which means T splits PQ into two equal parts. Those parts being PT and TQ.

Set them equal to each other and solve for x.

PT = TQ

3x+7 = 7x-9

3x-7x = -9-7

-4x = -16

x = -16/(-4)

x = 4

So,

PT = 3x+7 = 3*4+7 = 19

TQ = 7x-9 = 7*4-9 = 19

Both PT and TQ are 19 units long to help confirm the answer.

5 0
2 years ago
Read 2 more answers
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