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Firlakuza [10]
3 years ago
12

Help pls!! Solve the inequality x + 13 < 0. Give your answer in interval notation.

Mathematics
2 answers:
kotegsom [21]3 years ago
5 0

Answer:

-14

Step-by-step explanation:

x=-14+13

-1

0 is biger than -1

stiks02 [169]3 years ago
5 0
0 because it smaller than 1
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The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 63 minutes and a standard devi
oksano4ka [1.4K]

Answer:

a) X ~ N(63,18)

b) 0.5675 = 56.75%

c) 33.39 minutes

d) Q1: 50.85 minutes

Q3: 75.15 minutes

IQR: 24.3 minutes

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 = 63, \sigma = 18

A. X ~ N(63,18)

The mean and then the standard deviation.

B. Find the probability that a randomly selected person at the hot springs stays longer then an hour (60 minutes).

This is 1 subtracted by the pvalue of Z when X = 60. So

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

Z = \frac{60 - 63}{18}

Z = -0.17

Z = -0.17 has a pvalue of 0.4325

1 - 0.4325 = 0.5675

C. The park service is considering offering a discount for the 5% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount?

5th percentile, which is the value of X when Z has a pvalue of 0.05. So it is X when Z = -1.645.

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

-1.645 = \frac{X - 63}{18}

X - 63 = -1.645*18

X = 33.39

33.39 minutes

D. Find the Inter Quartile Range (IQR) for time spent at the hot springs.

Q1 = 25th percentile.

Value of X when Z has a pvalue of 0.25. So X when Z = -0.675

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

-0.675 = \frac{X - 63}{18}

X - 63 = -0.675*18

X = 50.85

Q1: 50.85 minutes

Q3 = 75th percentile

Value of X when Z has a pvalue of 0.75. So X when Z = 0.675

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

0.675 = \frac{X - 63}{18}

X - 63 = 0.675*18

X = 75.15

Q3: 75.15 minutes

IQR = Q3 - Q1:

75.15 - 50.85 = 24.3

IQR: 24.3 minutes

7 0
3 years ago
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