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Anika [276]
2 years ago
13

The weights of newborn babies are distributed normally, with a mean of approximately 105 Oz and a standard deviation of 15 Oz. I

f a newborn baby is selected at random. What if the probably that the baby weighs less than 150 Oz? help please!! Also I need to round answer to nearest thousandth
Mathematics
1 answer:
ICE Princess25 [194]2 years ago
7 0

Answer:

0.999 = 99.9% probability that the baby weighs less than 150 Oz.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

The weights of newborn babies are distributed normally, with a mean of approximately 105 Oz and a standard deviation of 15 Oz.

This means that \mu = 105, \sigma = 15

What if the probabability that the baby weighs less than 150 Oz?

This is the pvalue of Z when X = 150. SO

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

Z = \frac{150 - 105}{15}

Z = 3

Z = 3 has a pvalue of 0.999

0.999 = 99.9% probability that the baby weighs less than 150 Oz.

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Determine the margin of error for a 90% confidence interval to estimate the population mean when s = 40 for the sample sizes bel
Ann [662]

Answer:

a) The margin of error for a 90% confidence interval when n = 14 is 18.93.

b) The margin of error for a 90% confidence interval when n=28 is 12.88.

c) The margin of error for a 90% confidence interval when n = 45 is 10.02.

Step-by-step explanation:

The t-distribution is used to solve this question:

a) n = 14

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 14 - 1 = 13

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 13 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.9}{2} = 0.95. So we have T = 1.7709

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.7709\frac{40}{\sqrt{14}} = 18.93

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error for a 90% confidence interval when n = 14 is 18.93.

b) n = 28

27 df, T = 1.7033

M = T\frac{s}{\sqrt{n}} = 1.7033\frac{40}{\sqrt{28}} = 12.88

The margin of error for a 90% confidence interval when n=28 is 12.88.

c) The margin of error for a 90% confidence interval when n = 45 is

44 df, T = 1.6802

M = T\frac{s}{\sqrt{n}} = 1.6802\frac{40}{\sqrt{45}} = 10.02

The margin of error for a 90% confidence interval when n = 45 is 10.02.

3 0
2 years ago
Please solve and show working for 13-((4/5)+(6/8))=
UNO [17]
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This is your unsimplified answer
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Step-by-step explanation:

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kompoz [17]
\boxed {Question}
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\boxed {Cross \  multiply}
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\Longrightarrow \bf \ Answer \ : \ z = 7.2

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Step-by-step explanation:

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