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Jobisdone [24]
3 years ago
14

Suppose that we will randomly select a sample of 106 measurements from a population having a mean equal to 19 and a standard dev

iation equal to 7. Calculate the probability that we will obtain a sample mean less than 18.450; that is, calculate P( x < 18.450).
Mathematics
1 answer:
svet-max [94.6K]3 years ago
4 0

Answer:

z =\frac{18.45-19}{\frac{7}{\sqrt{106}}}= -0.809

And if we use the normal standard distribution or excel we got:

P(z

Step-by-step explanation:

For this case we have the following info given:

\mu = 19 represent the mean

\sigma = 7 represent the standard deviation

n = 106 represent the sample size

The distribution for the sample size if we use the central limit theorem (n>30) is given by:

\bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})

And for this case we want to find the following probability:

P(\bar X< 18.45)

And for this case we can use the z score formula given by:

z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing we got:

z =\frac{18.45-19}{\frac{7}{\sqrt{106}}}= -0.809

And if we use the normal standard distribution or excel we got:

P(z

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