What would the number 8671.42578125 ten be in IEEE 754 single precision floating point format. You need to follow the following
steps: a). Write the above number in binary. (before normalizing it) b). Write the above number in the normalized format. c). Compute the biased exponent, and write it in binary. d). Write its IEEE 754 single precision floating point format in binary, then in hex. (using 8 hex numbers)
1 answer:
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Answer:
0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
Find the probability that the average score of the 64 golfers exceeded 76.
This is 1 subtracted by the pvalue of Z when X = 64.
By the Central Limit Theorem
has a pvalue of 0.9772
1 - 0.9772 = 0.0228
0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.