The daily milk production of guernsey cows is approximately normally distributed with a mean of 35 kg/day and a std. deviation of 7 kg/day. the producer is concerned when the milk production of a cow falls below the 10th percentile since the animal may be ill. the 10th percentile (in kg) of the daily milk production is approximately:

The 10th percentile of the daily milk production is approximately 26.04kg.

Step-by-step explanation:

Problems of normally distributed samples can be 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.

In this problem, we have that:

The 10th percentile is the value of X when Z has a pvalue of 0.10. This is X when Z = -1.28. So

The 10th percentile of the daily milk production is approximately 26.04kg.

Step-by-step explanation:

Since the daily milk production of Guernsey cows is approximately normally distributed, we would apply the normal distribution formula which is expressed as

z = (x - u)/s

Where

x = daily milk production

u = mean milk production rate.

s = standard deviation

From the information given,

u = 35 kg/day

s = 7 kg/day.

The 10th percentile is 0.1. Looking at the normal distribution table, the z score corresponding to the 10th percentile is - 1.28

Therefore,

- 1.28 = (x - 35)/7

x - 35 = 7 × - 1.28

x - 35 = - 8.96

x = - 8.96 + 35

x = 26.04

The 10th percentile (in kg) of the daily milk production is approximately in 26 kg/day

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.