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laiz [17]
3 years ago
6

he heights of young women aged 20 to 29 follow approximately the N(64, 2.7) distribution. Young men the same age have heights di

stributed as N(69.3, 2.8).Height is measured in inches.A young woman in that age group is randomly selected; independently, a young man in that age group is randomly selected. What is the probability that the young man is taller than the young woman by more than 5 inches
Mathematics
1 answer:
natulia [17]3 years ago
8 0

Answer:

0.5319 = 53.19% probability that the young man is taller than the young woman by more than 5 inches

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

Z = \frac{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 p-value, we get the probability that the value of the measure is greater than X.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Distribution of the difference in height between men and woman:

Applying the concept above:

\mu = 69.3 - 64 = 5.3

\sigma = \sqrt{2.7^2 + 2.8^2} = 3.89

What is the probability that the young man is taller than the young woman by more than 5 inches?

Probability of the difference being more than 5 inches, that is, 1 subtracted by the pvalue of Z when X = 5.

Z = \frac{X - \mu}{\sigma}

Z = \frac{5 - 5.3}{3.89}

Z = -0.08

Z = -0.08 has a pvalue of 0.4681

1 - 0.4681 = 0.5319

0.5319 = 53.19% probability that the young man is taller than the young woman by more than 5 inches

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Find the sum of the first 47 terms of the following series, to the nearest integer.
topjm [15]

Answer:

The sum of the first 47 terms of the given series = 6016

Step-by-step explanation:

Given the sequence

13, 18, 23, ...

An arithmetic sequence has a constant difference 'd' and is defined by

a_n=a_1+\left(n-1\right)d

18-13=5,\:\quad \:23-18=5

As the difference between all the adjacent terms is the same.

so

d=5

a_1=13

Arithmetic sequence sum formula

n\left(a_1+\frac{d\left(n-1\right)}{2}\right)

Put the values

d=5

a_1=13

n=47

=47\left(13+\frac{5\left(47-1\right)}{2}\right)

=47\left(13+\frac{5\left(47-1\right)}{2}\right)

=47\left(13+115\right)

=47\cdot \:128

=6016

Thus, the sum of the first 47 terms of the given series = 6016

8 0
3 years ago
Emily and Holly took a road trip together. Emily drove at an average of 45 miles per hour for the first 3/7 of the total distanc
Elan Coil [88]
Emily drove 3/7 of the total distance and holly drove the rest which explains that holly drove 4/7 of the whole distance.

if 4 parts of the distance equals 24 miles, then 1 part would be 24/4 is 6.
since emily drove 3 parts of the whole distance, it is 6 × 3 = 18 miles.

travelling time of emily = 18/45 = 0.4 hr
travelling time of holly = 24/54 = 0.4 hr
--> total traveling time = 0.8 hr

i hope it is right
3 0
3 years ago
What is the product?
Lerok [7]
You just have to multiply straight across. Multiply the numerators for the new numerator, and the denominators for the new denominator.
5*3=15
4*8=32
15/32 is the answer (b).
5 0
3 years ago
Read 2 more answers
6 + 2x = 24
Nutka1998 [239]
<span>6 + 2x = 24
2x = 18
x = 9
answer
9
----------
</span><span>3x – 5 ≥ 7
3x </span>≥ 12
x ≥ 4
answer
<span>{4, 5, 6}
</span>
--------------
<span>4x – 3 ≥ 5
</span><span>4x  ≥ 8
</span><span>x  ≥ 2
answer
</span><span>{2, 3, 4}
</span>
-----------------

<span>3r ≤ 4r – 6
 r </span> ≥ 6
answer
<span>{6, 7, 8, 9,10}</span>
6 0
3 years ago
Xiaoming is making cookies. Each batch of cookies uses3 eggs. If Xiaoming has 20 eggs, and assuming he has enough of the other i
koban [17]

Answer:

6

Step-by-step explanation:

3(1)=3       3(2)=6          3(3)=9      3(4)=12     3(5)=15

3(6)=18     3(7)=21         3(8)=24

----------------------------------------------------

3(6)=18 is closest to 20

so the greatest number of batches Xiaoming can make is 6.

7 0
3 years ago
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