P=7r+3q <br> r= 5 and q= -4

The ages of adults in a certain community follow a normal distribution with mean 38 and standard deviation 6. The random variabl

nataly862011 [7]

Answer:

a = 33.32

Step-by-step explanation:

Problems of normally distributed samples are 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:

$\mu = 38, \sigma = 6$

P(32 < x < a) = .0590

This is the pvalue of Z when X = a subtracted by the pvalue of Z when X = 32.

X = 32

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

$Z = \frac{32 - 38}{6}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

X = a

p - 0.1587 = 0.0590

p = 0.0590 + 0.1587

p = 0.2177

So when X = a, Z has a pvalue of 0.2177. So when X = a, Z = -0.78.

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

$-0.78 = \frac{X - 38}{6}$

$X - 38 = -0.78*6$

$X = 33.32$

So a = 33.32

3 0

2 years ago

A circular running track is 1/2 a mile long. Elena runs on this track, completing each lap in 1/16 of an hour. What is Elena's r

goblinko [34]

Answer:

She completes a lap every 3 minutes and 45 seconds

Step-by-step explanation:

Divide 60 by 16.

8 0

2 years ago

The names of every month are written on separate pieces of paper and put into a basket. You draw a piece of paper at random. Fin

omeli [17]

Answer:

D

Step-by-step explanation:

Total Number of months = 12

How many start from J = 3

Probability= 3/12

= 1/4

Answer from Gauthmath

4 0

2 years ago

A manufacturer sells mirrors in the shapes of squares. The smallest size mirror the manufacturer sells has an area of 4 ft ^2. T

tester [92]

The domain of the graph of the that represents the side length of the mirror is 2 ≤ x ≤3

<h3>How to determine the graph?</h3>

The given parameters are:

Shape = Square
Smallest area = 4ft²
Largest area = 9ft²

The area (y) of a square of side length x is:

y = x²

Make x the subject

x = √y

When y = 9, we have:

x = √9 = 3

When y = 4, we have:

x = √4 = 2

This means that the domain of the graph of the that represents the side length of the mirror is 2 ≤ x ≤3

See attachment for the graph

P=7r+3q r= 5 and q= -4