Ralph and Melissa watch lots of videos. But they have noticed that they don't agree very often. In fact, Ralph only likes about 10% of the movies that Melissa likes, i.e., P(Ralph likes a movie|Melissa likes the movie) = .10 They both like about 37% of the movies that they watch. (That is, Ralph likes 37% of the movies he watches, and Melissa likes 37% of the movies she watches.) If they randomly select a movie from a video store, what is the probability that they both will like it? prob. =

Answers

Answer 1
Answer:

Answer:

There is a 3.7% probability that they both will like it.

Step-by-step explanation:

We can solve this problem using the Bayes rule derivation from conditional probability.

Bayes rule:

What is the probability of B, given that A?

P(A/B) = (P(A \cap B))/(P(A))

In this problem, we have that:

P(A/B) is the probability that Ralph likes the movie, given that Melissa likes. The problem states that this is 10%. So P(A/B) = 0.1

P(A) is the probability that Melissa likes the movie. The problem states that P(A) = 0.37.

If they randomly select a movie from a video store, what is the probability that they both will like it?

This is P(A \cap B).

P(A/B) = (P(A \cap B))/(P(A))

P(A \cap B) = P(A)*P(A/B)

P(A \cap B) = 0.37*0.10 = 0.037

There is a 3.7% probability that they both will like it.


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The test statistic of zequalsnegative 2.40 is obtained when testing the claim that less than 0.32. a. Using a significance level of alphaequals0.10​, find the critical​ value(s). b. Should we reject Upper H 0 or should we fail to reject Upper H 0​

Answers

Answer:

a) Critical value = -1.285

b) We should reject null hypothesis that the mean equals 0.32

Step-by-step explanation:

Given that the  statistic of z equals negative 2.40 is obtained when testing the claim that less than 0.32

i.e. for hypotheses

H_0: \bar = 0.32\nH_a: \bar x <0.32\n

(one tailed test at 10% significance level)

Z critical value for 90% one tailed = -1.285

Since our test statistic is less than -1.285 we reject null hypothesis

a) Critical value = -1.285

b) We should reject null hypothesis that the mean equals 0.32

A resident of Bayport claims to the City Council that the proportion of Westside residents (1) with income below the poverty level is lower than the proportion of Eastside residents
(2) The City Council decides to test this claim by collecting a random sample of resident incomes from the Westside of town and a random sample of resident incomes from the Eastside of town. Seventy-six out of 578 Westside residents had an income below the poverty level. Hundred-and-twelve out of 688 Eastside residents had an income below the poverty Specify the hypotheses.
Calculate the value of the test statistic (round to 4 decimal places).
Calculate the p-value (round to 4 decimal places).

Answers

Answer:

The test statistics is  z =  -1.56  

The p-value is   p-value =  0.05938

Step-by-step explanation:

From the question we are told  

   The West side sample  size is n_1  =  578

    The  number of residents on the West side with income below poverty level is k  = 76

    The East side sample size  n_2=688

  The  number of residents on the East side with income below poverty level is u  = 112

   The null hypothesis is  H_o  :  p_1 = p_2

    The alternative hypothesis is  H_a :  p_1 <  p_2

Generally the sample proportion of  West side is  

     \^(p) _1 = (k)/(n_1)

=>   \^(p) _1 = (76)/(578)

=>   \^(p) _1 =  0.1315

Generally the sample proportion of  West side is  

     \^(p) _2 = (u)/(n_2)

=>   \^(p) _2 = (112)/(688)

=>   \^(p) _2 =  0.1628

 Generally the pooled sample proportion is mathematically represented as

    p = (k + u)/( n_1 + n_2 )

=>  p = (76 + 112)/( 578 + 688 )

=>  p =0.1485

Generally the test statistics is mathematically represented as

z = \frac{\^ {p}_1 - \^(p)_2}{\sqrt{p(1- p) [(1)/(n_1 ) + (1)/(n_2)  ]}  }

=> z = \frac{ 0.1315  - 0.1628 }{\sqrt{0.1485(1-0.1485) [(1)/(578) + (1)/(688)  ]}  }  

=> z =  -1.56  

Generally the p-value  is mathematically represented as

          p-value =  P(z <  -1.56 )

From z-table  

         P(z <  -1.56 ) =  0.05938

So

     p-value =  0.05938

Disk requests come in to the disk driver for cylinders 10, 22, 20, 2, 40, 6, and 38, in that order. A seek takes 6 msec per cylinder. How much seek time is needed for (a) First-come, first served. (b) Closest cylinder next. (c) Elevator algorithm (initially moving upward). In all cases, the arm is initially at cylinder 20.

Answers

Answer:

Step-by-step explanation:

The order for FCFS is: 20->10->22->20->2->40->6->38.

Distance is

10+12+2+18+38+34+32 = 146

cylinders, so time is

146* 6 = 876 sec.

The order for elevator is:

20->20->22->38->40->10->6->2.

Distance is

0+2+16+2+30+4+4 = 58

cylinders, so time is

58 * 6 =348 msec.

The order for CCN is:

20->20->22->10->6->2->38->40.

Distance is

0+2+12+4+4+36+2 = 60

cylinders, so time is 60 * 6 =360 msec.

Combine the like terms to create an equivalent expression:
−4p+(−2)+2p+3

Answers

Answer:

-2p+1

Step-by-step explanation:

combine -4p+2p=-2p and -2+3=1 so your answer is -2p+1

In a triangle, the measure of the second angle is twice the measure of the first angle. The third angle is equal to the sumof the other angles,
Which of the following could represent the measures of the three angles?
Ox, 2%, 4%
OX, 2x, 3x
OX, 2x, 2x

Answers

Answer:

x, 2x, 3x

Step-by-step explanation:

If we have angle x as one angle, and the 2nd angle is twice the angle, the 2nd angle will be 2x. If the 3rd angle is the sum of the 1st angle and the 2nd angle, we have 2x + x, which equals 3x.

Solve for x.
7x = 42

Answers

Answer:

x = 6

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

7x=42

X divided by 7 and 42 divided by 7 gives you

x=6