Which inequality is graphed in blue

Assume that foot lengths of women are normally distributed with a mean of 9.6 in and a standard deviation of 0.5 in.a. Find the

Makovka662 [10]

Answer:

a) 78.81% probability that a randomly selected woman has a foot length less than 10.0 in.

b) 78.74% probability that a randomly selected woman has a foot length between 8.0 in and 10.0 in.

c) 2.28% probability that 25 women have foot lengths with a mean greater than 9.8 in.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 9.6, \sigma = 0.5$ .

a. Find the probability that a randomly selected woman has a foot length less than 10.0 in

This probability is the pvalue of Z when $X = 10$ .

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

$Z = \frac{10 - 9.6}{0.5}$

$Z = 0.8$

$Z = 0.8$ has a pvalue of 0.7881.

So there is a 78.81% probability that a randomly selected woman has a foot length less than 10.0 in.

b. Find the probability that a randomly selected woman has a foot length between 8.0 in and 10.0 in.

This is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 8.

When X = 10, Z has a pvalue of 0.7881.

For X = 8:

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

$Z = \frac{8 - 9.6}{0.5}$

$Z = -3.2$

$Z = -3.2$ has a pvalue of 0.0007.

So there is a 0.7881 - 0.0007 = 0.7874 = 78.74% probability that a randomly selected woman has a foot length between 8.0 in and 10.0 in.

c. Find the probability that 25 women have foot lengths with a mean greater than 9.8 in.

Now we have $n = 25, s = \frac{0.5}{\sqrt{25}} = 0.1$ .

This probability is 1 subtracted by the pvalue of Z when $X = 9.8$ . So:

$Z = \frac{X - \mu}{s}$

$Z = \frac{9.8 - 9.6}{0.1}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772.

There is a 1-0.9772 = 0.0228 = 2.28% probability that 25 women have foot lengths with a mean greater than 9.8 in.

5 0

3 years ago

MATT plans to put concrete on a regular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of conc

Ivanshal [37]

THIS IS THE COMPLETE QUESTION BELOW;

Matt plans to put concrete on a rectangular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Matt needs is $58.07. Which of the following is closest to the width of the portion of the driveway on which Matt plans to put concrete?. . [1 foot = 12 inches; 1 yard = 3 feet]. a. 0.5 feet. b. 1.5 feet. c. 3 feet. d. 6 feet

Answer:

OPTION D is correct

d)6feet

Step by step Explanation:

We were given The price of concrete as $98 per cubic yard

Price= $98 /yrd³

But 1 foot = 12 inches

1 yard = 3 feet

Square both side we have,

Then 1yrd³ = 27 ft³.

So we can use this conversion factor to convert $98 /yrd³ to per ft³ as follows

$98 /yd³) ×(1 yrd³ / 27 ft³) = $ 98/27/ft³

If we denote the width of the portion as "y"

then the volume of the rectangular portion of the driveway =

= (8 ft) (1/3 ft) x = 8y/3 ft³

But we're given The total cost of the concrete Matt needs as $58.07,

Total cost = $58.07 = (8y/3)(98/27)

y= 5.99957 ft= 6feet

Therefore, the width of the portion of the driveway is 6feet

6 0

2 years ago

What are the missing measurements?

amm1812

Answer:

A B AND C SQUERA

Step-by-step explanation:

4 0

2 years ago

How to find the value of X

Mekhanik [1.2K]

Where is the question

4 0

3 years ago

Read 2 more answers

Use the formula for the amount, a = p(1 + rt), to find the indicated quantity.

Alexeev081 [22]

a= p(1+rt)

a= $4,100(1+12%×2×0.25)

a= $4,100×(1+6%) 100%=1 -> 6%= 0,06

a= $4,100×1,06

a= $4,346

5 0

2 years ago