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tino4ka555 [31]
3 years ago
15

Assume that the ages for first marriages are normally distributed with a mean of 26 years and a standard deviation of 4 years. W

hat is the probability that a person getting married for the first time is in his or her twenties? (Round your answer to 4 decimal places.)
Mathematics
1 answer:
Snowcat [4.5K]3 years ago
6 0

Answer:

0.7743

Step-by-step explanation:

Mean of age = u = 26 years

Standard Deviation = \sigma = 4 years

We need to find the probability that the person getting married is in his or her twenties. This means the age of the person should be between 20 and 30. So, we are to find P( 20 < x < 30), where represents the distribution of age.

Since the data is normally distributed we can use the z distribution to solve this problem. The formula to calculate the z score is:

z=\frac{x-u}{\sigma}

20 converted to z score will be:

z=\frac{20-26}{4}=-1.5

30 converted to z score will be:

z=\frac{30-26}{4}=1

So, now we have to find the probability that the z value lies between -1.5 and 1.

P( 20 < x < 30) = P( -1.5 < z < 1)

P( -1.5 < z < 1 ) = P(z < 1) - P(z<-1.5)

From the z-table:

P(z < 1) = 0.8413

P(z < -1.5) =0.067

So,

P( -1.5 < z < 1 ) = 0.8413 - 0.067 = 0.7743

Thus,

P( 20 < x < 30) = 0.7743

So, we can conclude that the probability that a person getting married for the first time is in his or her twenties is 0.7743

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If two marbles are selected at random with replacing between draws, what is the probability that the outcome is red then yellow?
saul85 [17]

The probability that the outcome is red then yellow is 0.036.

Given that in a jar there are 8 red marbles, 1 yellow marble and 6 green marbles.

We are required to find the probability of obtaining a red then yelow marble if two marbles are drawn and replacement is used.

Probability is the calculation of finding the chance of happening a event among all the events possible. It lies between 0 and 1.

Probability=Number of items/ Total items.

Number of red marbles=8

Number of yellow marble=1

Number of green marbles=6

Total marbles=15

Probability of obtaining red marble=8/15

Probability of obtaining yellow marble=1/15 (Because replacing is there so the number of total marbles do not decrease)

Required probability=8/15*1/15

=8/225

=0.035555

After rounding off we will get 0.036.

Hence the probability that the outcome is red then yellow is 0.036.

Question is incomplete. The following line should be included in question:

A jar contains 8 red marbles , a yellow marble and 6 green marbles.

Learn more about probability at brainly.com/question/24756209

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