Question

Suppose you are working with a data set that is normally distributed with a mean of 70 and a standard deviation of 10. Determine the value of x such that 65% of the values are greater than x. Select one: a. 60 b. 80 c. 74 d. 66

Answer 1

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Answer:

60

Answer 2

Find the value of 'x' for given normal distribution for the given situation

Explanation:

• You want to find the value of 'x' where $65\%$ of the values lie above it.
• In other words, you want to find the $(100-65)=35^{th}$ percentile of 'x'.
• First, you need to find the $35^{th}$ percentile for 'z' (using the Z-table available on any search engine).
• Then change the z-value to an x-value by using the z-formula: $z=\frac{x-\mu}{\sigma}$  
• To find the $35^{th}$ percentile for 'z' and find the probability that's closest to $0.35$. The probabilities from the Z-table are the values inside the table.
• From the Z-table, the closest probability to $0.35$ is $0.3483$. Its corresponding row is $-0.3$ and column is $-0.09$.
• Put these numbers together and to get the z-score of $z=-0.39$.
• now we have , $\mu=70\ \ \ \ \ \sigma=10\ \ \ \ \ z=-0.39$ hence we get                                   $z=\frac{x-\mu}{\sigma} \\-0.39=\frac{x-70}{10} \\x=70-3.9= 66.1\\->x= 66(approx.)$            --------ANSWER
• The value of 'x' for $65\%$ of values to be greater than it is option (d)$66$.