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Helen [10]
3 years ago
14

For some postive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770. The value of Z is

Mathematics
1 answer:
Talja [164]3 years ago
8 0

Answer:

1.16

Step-by-step explanation:

Given that;

For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770.

This implies that:

P(0<Z<z) = 0.3770

P(Z < z)-P(Z < 0) = 0.3770

P(Z < z) = 0.3770 + P(Z < 0)

From the standard normal tables , P(Z < 0)  =0.5

P(Z < z) = 0.3770 + 0.5

P(Z < z) =  0.877

SO to determine the value of z for which it is equal to 0.877, we look at the

table of standard normal distribution and locate the probability value of 0.8770. we advance to the  left until the first column is reached, we see that the value was 1.1.  similarly, we did the same in the  upward direction until the top row is reached, the value was 0.06.  The intersection of the row and column values gives the area to the two tail of z.   (i.e 1.1 + 0.06 =1.16)

therefore, P(Z ≤ 1.16 ) = 0.877

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The volume of the ball is 33.5 cubic centimeter.

<u>Step-by-step explanation:</u>

It is given that, a ball has a radius of 8 cm.

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To find the volume of the ball, you need to use the formula for volume of the sphere.

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==================================================

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