10 PTS AND MARK BRAINLEST!!!! PLZZZZ HELLLPPP!!!!

A motel has a policy of booking as many as 150 guests in a building that holds 140. Past studies indicate that only 85% of booke

iren2701 [21]

Answer:

0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ , if $np \geq 10$ and $n(1-p) \geq 10$ .

150 guests booked:

This means that $n = 150$

85% of booked guests show up for their room.

This means that $p = 0.85$

Is the normal approximation suitable:

$np = 150(0.85) = 127.5$

$n(1-p) = 150(0.15) = 22.5$

Both greater than 10, so yes.

Mean and standard deviation:

$\mu = E(X) = np = 150*0.85 = 127.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.85*0.15} = 4.3732$

Find the probability that if the motel books 150 guests, not enough seats will be available.

More than 140 show up, which, using continuity correction, is $P(X > 140 + 0.5) = P(X > 140.5)$ , which is 1 subtracted by the p-value of Z when X = 140.5. So

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

$Z = \frac{140.5 - 127.5}{4.3732}$

$Z = 2.97$

$Z = 2.97$ has a p-value of 0.9985.

1 - 0.9985 = 0.0015.

0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.

5 0

3 years ago

In two years, Linda will be half as old as her mother. Her mother is 38 years old now. Let L = the age of Linda now. Which formu

shutvik [7]

IDk but ill trry to put the formula..chose what evers closest to this --> 1/2*38=L L= 19

5 0

3 years ago

PL HELP ME GIVING 100

il63 [147K]

Answer:

C ≤ 11

Step-by-step explanation:

c − 5.5 + 5.5 ≤ 5.5 + 5.5

add 5.5 to both sides

8 0

3 years ago

Read 2 more answers

Given: △ABC, m∠C=90° m∠ABC=30°, AL ∠ bisector CL=6 ft. Find: LB

vlada-n [284]

For a better understanding of the solution given here please go through the diagram in the file attached.

To solve this question we will make use of the "Triangle Angle Bisector Theorem", which states that, "An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle."

Thus, in our question, we will have:

$\frac{LB}{CL}= \frac{AB}{AC}$