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Nadya [2.5K]
3 years ago
7

In a data set with a normal distribution, the mean is 59 and the standard deviation is 3.

Mathematics
1 answer:
lakkis [162]3 years ago
5 0

Answer:

a) P(53

P(-2

P(-2

b) a=59 +1.96*3=64.88

And for the other limit we have:

a=59 -1.96*3=53.12

And we will have 95% of the values between (53.12, 64.88)

Step-by-step explanation:

Part a

Let X the random variable of interest of a population, and for this case we know the distribution for X is given by:

X \sim N(59,3)  

Where \mu=59 and \sigma=3

We are interested on this probability :

P(53

And we can solve this using the z score:

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

Using the last formula we got:

P(53

And we can find this probability with this difference:

P(-2

And uing the normal standard distribution or excel we got:

P(-2

Part b

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.025   (a)

P(X   (b)

As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.96.

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.96

And if we solve for a we got

a=59 +1.96*3=64.88

And for the other limit we have:

a=59 -1.96*3=53.12

And we will have 95% of the values between (53.12, 64.88)

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