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Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. 85% of the possible Z values are smaller than . Use your z-table and give your answer to 2 decimal places. Find the area under the standard normal curve that lies to the right of -0.91. Calculate answers to four decimal places. The variable X is normally distributed with μ = 61.00 and σ = 13.00. Determine the z-score for the randomly chosen value 76.00. Round your z-score to 2 decimal places. Find the area under the standard normal curve that lies in between -5.10 and 1.0. Calculate answers to four decimal places. Determine the z-value that has area 0.9922 to the left. (Report the z-value to 2 decimal places.)



Answer :

To find the area under the standard normal curve that lies to the right of -0.91, we can use a z-table to look up the corresponding probability. We find that the area to the right of -0.91 is approximately 0.1587.

To find the z-score for the value 76.00, we can use the formula for a z-score: (x - μ) / σ. Plugging in the values given, we get: (76.00 - 61.00) / 13.00 = 2.77. So the z-score for the value 76.00 is approximately 2.77.

To find the area under the standard normal curve that lies between -5.10 and 1.0, we can use a z-table to find the corresponding probabilities for each of these values and then subtract the probability for -5.10 from the probability for 1.0. We find that the probability of -5.10 is approximately 0.0000, and the probability of 1.0 is approximately 0.8413. Subtracting these values gives us an area of approximately 0.8413.

To find the z-value that has an area of 0.9922 to the left, we can use a z-table to look up the corresponding z-value. We find that the z-value that corresponds to an area of 0.9922 to the left is approximately  2.33.

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