1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andrezito [222]
3 years ago
6

A population of values has a normal distribution with μ = 155.4 and σ = 49.5 . You intend to draw a random sample of size n = 24

6 . Find the probability that a single randomly selected value is between 158.6 and 159.2. P(158.6 < X < 159.2) = .0048 Correct Find the probability that a sample of size n = 246 is randomly selected with a mean between 158.6 and 159.2. P(158.6 < M < 159.2) = .0410 Correct
Mathematics
2 answers:
xz_007 [3.2K]3 years ago
4 0

Answer:

(a) The probability that a single randomly selected value lies between 158.6 and 159.2 is 0.004.

(b) The probability that a sample mean is between 158.6 and 159.2 is 0.0411.

Step-by-step explanation:

Let the random variable <em>X</em> follow a Normal distribution with parameters <em>μ</em> = 155.4 and <em>σ</em> = 49.5.

(a)

Compute the probability that a single randomly selected value lies between 158.6 and 159.2 as follows:

P(158.6 < X

*Use a standard normal table.

Thus, the probability that a single randomly selected value lies between 158.6 and 159.2 is 0.004.

(b)

A sample of <em>n</em> = 246 is selected.

Compute the probability that a sample mean is between 158.6 and 159.2 as follows:

P(158.6 < \bar X

*Use a standard normal table.

Thus, the probability that a sample mean is between 158.6 and 159.2 is 0.0411.

Marizza181 [45]3 years ago
3 0

Answer:

(a) P(158.6 < X < 159.2) = 0.0048

(b) P(158.6 < M < 159.2) = 0.041

Step-by-step explanation:

We are given that a population of values has a normal distribution with μ = 155.4 and σ = 49.5.

(a) <em>Let X = a single randomly selected value</em>

So, X ~ N(\mu=155.4,\sigma^{2} = 49.5^{2})

The z-score probability distribution for single selected value is given by;

                Z = \frac{X-\mu}{\sigma}  ~ N(0,1)

where, \mu = population mean = 155.4

            \sigma = standard deviation = 149.5

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, probability that a single randomly selected value is between 158.6 and 159.2 is given by =  P(158.6 < X < 159.2) = P(X < 159.2) - P(X \leq 158.6)

    P(X < 159.2) = P( \frac{X-\mu}{\sigma} < \frac{159.2-155.4}{49.5} ) = P(Z < 0.077) = 0.5307

    P(X \leq 158.6) = P( \frac{X-\mu}{\sigma} \leq \frac{158.6-155.4}{49.5} ) = P(Z \leq 0.065) = 0.5259                                    

<em>The above probabilities is calculated by looking at the value of x = 0.077 and x = 0.065 in the z table which has an area of 0.5307 and 0.5259 respectively.</em>

Therefore, P(158.6 < X < 159.2) = 0.5307 - 0.5259 = 0.0048

(b) Now we are given a sample size of 246.

<em>Let M = sample mean </em>

The z-score probability distribution for sample mean is given by;

                Z = \frac{ M -\mu}{{\frac{\sigma}{\sqrt{n} } }} }  ~ N(0,1)

where, \mu = population mean = 155.4

            \sigma = standard deviation = 149.5

            n = sample size = 246

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, probability that the mean is between 158.6 and 159.2 is given by =  P(158.6 < M < 159.2) = P(M < 159.2) - P(M \leq 158.6)

    P(M < 159.2) = P( \frac{ M -\mu}{{\frac{\sigma}{\sqrt{n} } }} } < \frac{ 159.2-155.4}{{\frac{49.5}{\sqrt{246} } }} } ) = P(Z < 1.20) = 0.885

    P(M \leq 158.6) = P( \frac{ M -\mu}{{\frac{\sigma}{\sqrt{n} } }} } \leq \frac{ 158.6-155.4}{{\frac{49.5}{\sqrt{246} } }} } ) = P(Z \leq 1.01) = 0.844                                      

<em>The above probabilities is calculated by looking at the value of x = 1.20 and x = 1.01 in the z table which has an area of 0.885 and 0.844 respectively.</em>

Therefore, P(158.6 < M < 159.2) = 0.885 - 0.844 = 0.041

You might be interested in
Product A is an 8 oz bottle of cough medication that sells for $1.36. Product B is a 16 oz bottle of cough medication that costs
kvasek [131]
Product A. Is $0.17 per ounce. Product B. Is $0.20 per ounce. Product A. Is cheaper by the ounce. Please mark brainliest.
3 0
3 years ago
What part of 8 is 64
aev [14]

Answer:

I believe the answer would be 1/8 of 64

Step-by-step explanation:

I think it means what fraction of 64 is 8, so in that case, 8 would be 1/8 of 64.

3 0
2 years ago
Read 2 more answers
What does ‘b” represent in y=mx+b
tigry1 [53]

Answer:

In the equation y = mx + b for a straight line, the. number b is called the y-intercept of the line.

Step-by-step explanation:

5 0
3 years ago
Which expression is equivalent to 1/3?
taurus [48]

Answer:

C) 1/6y+1/6(y+12)-2

Step-by-step explanation:

5 0
2 years ago
(f^3-5f+25)-(4f^2-12f+9)
pochemuha

Answer:

3−42+7+16

Step-by-step explanation:

if its simplify

8 0
3 years ago
Other questions:
  • How do you use the slope to prove lines are parallel or perpendicular?
    9·1 answer
  • Filiate<br> Consider the line MU for M(-1, 1) and U(4, 5).<br> what’s the distance from M to U ?
    10·2 answers
  • PLEASE HELP ASAP FOR 10 and 11 (SHOW WORK+LOTS OF POINTS)
    7·2 answers
  • Ribbon is sold at 3 yards for 6.33. Jackie bought 24 yards of ribbon for a project. How much did he pay?
    13·2 answers
  • line segments AB has endpoints A(9,3) and B(2,6). Find the coordinates of the point that divides the line segment directed from
    5·1 answer
  • Write a solution to the equation x? = 75 two<br> ways:<br> using exponents<br> using radicals
    12·1 answer
  • 49 – 3m = 4m + 14 please help
    14·1 answer
  • Find (f • g)(-1).<br> f(x) = x + 1<br><br> g(x) = x^2 + 5x
    9·2 answers
  • Please help my with this question!!! I’ll give brainlist for the correct answer
    10·2 answers
  • if 1/3 of a gallon of orange juice is shared equally between 4 friends how much orange juice will each friend receive?​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!