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Veseljchak [2.6K]
3 years ago
15

A population has a mean muequals160 and a standard deviation sigmaequals20. Find the mean and standard deviation of the sampling

distribution of sample means with sample size nequals58
Mathematics
1 answer:
hoa [83]3 years ago
6 0

Answer:

Mean 160

Standard deviation 2.63

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 160, \sigma = 20

Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 58.

Mean 160

Standard deviation s = \frac{20}{\sqrt{58}} = 2.63

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Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value t
allochka39001 [22]

Answer:

Neither the normal distribution nor the t distribution applies.

Step-by-step explanation:

Hello!

The histogram attached shows the salary (in dollars) of 63 football players.

As you can see most of the values of this distribution are around 0 and the distribution is extremely asymmetrical (right skewed).

To apply a t-test to study the population average the population has to have a normal distribution.

The same goes for the standard normal distribution, but in this case, considering that the sample is large enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample mean to normal X[bar]≈N(μ;δ²/n), but since the population variance is unknown, this is also not applicable.

The correct choice is the last one, since the conditions to apply the t test and the standard normal are not met.

I hope this helps!

6 0
3 years ago
Arlen receives of $590 per week plus a 5% commission on all sales over
Vladimir79 [104]

Answer:

$651.50

Step-by-step explanation:

Anything OVER 650 is paid in commissions.

Since total sales was 1880, the amount paid in commissions is:

1880 - 650 = $1230

Arlen will get 5% of 1230, that is:

5/100 = 0.05

0.05 * 1230 = $61.5

Weekly Pay = 590

Commissions = 61.5

Total Pay = 590 + 61.5 = $651.50

Last option is right.

6 0
3 years ago
Find the radius of a circle that has this measurement. d=2.25cm
yuradex [85]
I would say your answer would be  1.125 because the radius is half of the diameter so 2.25 / 2  gives you 1.125.
6 0
3 years ago
At age 9, Gerald is 5 feet tall. If he grows at a rate of 1.5 inches per year, how old will he be when he hits 6 feet?
creativ13 [48]

Step-by-step explanation:

he will be 17. he is going to grow 1.5 inch per year, if we do 1.8×8= 12.0 or 1 ft so it will take him 8 years to be 6feet

8 0
3 years ago
The lengths of adjacent sides of a rectangle are 572 units and 8,2
Varvara68 [4.7K]

Answer:

13 units

Step-by-step explanation:

Giveb that :

Perimeter = 5/2 + 8/2 + 5/2 + 8/2

Hence, sum of the perimeter will be ;

The L. C. M of the denominator = 2

(5 + 8 + 5 + 8) / 2

= 26 / 2

= 13 units

Hence, the perimeter of the rectangle is 13 units

8 0
2 years ago
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